_ _ _ _ _ _ _ _ Class name _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

First, multiple-choice questions:

1, quadratic function y=x2-( 12-k)x+ 12, when x >；; At 1, y increases with the increase of x, and when x

12(B) 1 1(C) 10(D)9

2, in the following four functions, y value decreases with the increase of x value is ().

(A) (B) (C) (D)

3. If the image of quadratic function y=ax2+bx passes through point A (-1, 1), then ab has ().

(a) Minimum value 0 (B) Maximum value 1 (C) Maximum value 2 (D) has the minimum value.

4. The image of parabola y=ax2+bx+c is as shown in the figure, OA=OC, then ()

(a) AC+1= b (b) AB+1= c (c) BC+1= A (d) None of the above.

5. If the vertex of the quadratic function y=ax2+bx+c is in the first quadrant and passes through points (0, 1) and (-1, 0), then the value range of S=a+b+c is ().

(A)0 & lt； S & lt2(B)S & gt； 1 (C) 1<S & lt2(D)- 1 & lt； S & lt 1

6. If the distance from the vertex of the parabola y=x2-6x+c-2 to the X axis is 3, then the value of c is equal to ().

(A)8 (B) 14 (C)8 or 14 (D)-8 or-14.

7. Translate the image of quadratic function by 2 units to the left, and then translate it up by 1 unit. The quadratic function relation of the obtained image is ().

(A) (B) (C) (D)

8.(3) If the parabola y=ax2+bx is known, when a >; 0, b<0, whose image passes ()

A. Quadrants one, two and three B. Quadrants one, two and four

C. quadrants one, three and four d. Quadrants one, two, three and four

9, if, the vertex of the quadratic function image in ()

(a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant

10, known quadratic function, constant, when y reaches the minimum value, the value of x is ().

(A) (B) (C) (D)

1 1, when a>0, b<0, c>0, the following images may be parabola y=ax2+bx+c ().

12. No matter what the value of x is, the condition that the value of function y=ax2+bx+c(a≠0) is always greater than 0 is ().

A.a & gt0，△& gt； 0b . a & gt； 0，△& lt； 0 C.a & lt0，△& lt； 0d . a & lt； 0，△& lt； 0

Second, fill in the blanks:

13 As shown in the figure, it is known that the point M(p, q) is on the parabola y = x2- 1, the circle centered on m intersects the X axis at two points A and B, and the abscissas of the points A and B are two of the equations x2-2px+q = 0 about X, then the chord length AB is equal to.

14, let x, y and z satisfy the relation x- 1 = =, then the minimum value of x2+y2+z2 is.

On the image of 15 with known quadratic function y = ax2 (a ≥ 1), the abscissas of points A and B are-1 and 2 respectively, and point O is the coordinate origin. If △AOB is a right triangle, the circumference of △OAB is.

16. It is known that the abscissa of the intersection of the quadratic function y =-4x2-2mx+m2 and the inverse proportional function y = in the second quadrant is -2, so the value of m is.

17, the quadratic function is known. When x = _ _ _ _ _ _ _ the function reaches the minimum value.

18. There is a parabolic arch bridge with a maximum height of 16m and a span of 40m. Now put its schematic diagram in the plane rectangular coordinate system as shown in Figure (4), and the analytical formula for finding parabola is _ _ _ _ _ _ _ _ _ _ _ _.

19 as shown in figure (5), A.B.C is three points on the image of quadratic function Y = AX2+BX+C (A ≠ 0). According to the positions of the three points given in the figure, A-0, C-0 and ⊿-0 can be obtained.

20. The teacher gave a function. Four students, A, B, C and D, each pointed out a property of this function: A: The image of the function does not pass through the third quadrant.

B: The image of the function passes through the first quadrant. C: When x < 2, Y decreases with the increase of X. D: When x < 2, y > 0, we can see that these four students' statements are correct. Please construct a function _ _ _ _ _ _ _ _ _ _ _.

2 1, it is known that the image of the quadratic function y = x2+bx+c passes through the point a (c, 0) and is symmetrical about the straight line x=2, then the analytic formula of this quadratic function may be ————————— (just write a possible analytical formula).

22. The functional relationship between flying height h(m) and flying time t(s) is h = v0tsinα-5t2, where v0 is the initial launching speed of the shell and α is the launching angle of the shell. When v0=300 (), sinα= sinα =, and the maximum flying height of the projectile is _ _ _ _ _ _ _.

23, parabola y=-(x-L)(x-3-k)+L and parabola y=(x-3)2+4 are symmetrical about the origin, then l+k = _ _ _ _ _.

Third, answer questions:

23. It is known that the abscissas of the two intersections between the image of quadratic function Y = x2+bx+c and the X axis are x 1 and X2, respectively. The two real roots of quadratic equation X2+B2X+20 = 0 are x3 and x4, and X2-X3 = X 1-X4 = 3. Find the analytic expression sum of quadratic function

24. In 2000, Shen Ying Automobile Refitting Factory of Dongfeng Company developed Type A agricultural vehicles with a cost of 20,000 yuan/vehicle, an ex-factory price of 24,000 yuan/vehicle and an annual sales price of 1 10,000 vehicles. In order to support the construction of ecological agriculture in the western development, the factory seized the opportunity of developing enterprises, comprehensively improved the scientific and technological content of type A agricultural vehicles, and raised the cost price of each agricultural vehicle.

(1) Find out the functional relationship between the annual profit y (ten thousand yuan) and X from the sales situation of type A agricultural vehicles in this factory in 200 1 year.

(2) If the annual profit of selling Type A agricultural vehicles in 200 1 year reaches 40.28 million yuan, how many vehicles should be sold in that year?

25. As the picture shows, there is a parabolic arch bridge. The width of AB under the bridge is 20m at normal water level. When the water level rises by 3 meters, it reaches the warning line CD. This is the water surface width of 10m. (1) Find the analytical formula of parabola in the coordinate system as shown in the figure.

(2) If the water level rises at the rate of 0.2m per hour when the flood comes, how many hours will it last from the warning line to the top of the arch bridge?

26. When the car is running, it will slide forward for a certain distance after braking before stopping. We call this distance "braking distance", which is an important factor in analyzing accidents. On a curve with a speed limit of 40 b, two cars, A and B, walked in opposite directions and found that the situation was wrong. Brake at the same time, but still collided. Afterwards, the braking distance of a car was measured at the scene as 12m. The braking distance of car B is greater than 10m, but less than 20m. According to relevant data, the braking distance S A (m) of car A has the following relationship with the vehicle speed X (), where S A = 0. 1x+0.0 1x2. The relationship between the braking distance S B (m) of car B and the vehicle speed X () is shown in the following figure.

.

27. Since the reform and opening up, a town has developed its local economy through multiple channels, with a gross national product of 200 million yuan in 1995. According to estimates, when the gross national product of this town is 500 million yuan, it can reach a well-off level.

(1) If 1996 starts, the town's gross national product will increase by 60 million yuan every year compared with the previous year, how many years will it take for the town to reach a well-off level?

(2) Taking 200 1 as the first year, the town's gross national product in X year is Y billion yuan, and the relationship between Y and X is y= (x≥0). Can the town's GNP quadruple on the basis of 1995 (that is, reach four times the annual GNP 1995)?

28. It is known that the quadratic function intersects the X axis at two points, that is, the point M (x 1, 0) n (x2, 0) and the Y axis intersect at the point h,

(1) If ∠HMO = 450∠MHN = 1050, ask: Resolution function;

(2) If, when point Q(b, c) is on a straight line, find the analytic expression of quadratic function.

29. it is known that the function y=-ax2+bx+c(a≠0) passes through the image points p (- 1, 2) and q (2, 4).

(1) proves that the intersection of parabolic image and X axis is on both sides of the origin, whether A is any real number or not; If its image has two intersections with the X axis, and A and B(A is on the left of B) intersect with the Y axis at point C, find the parabolic analytical formula;

(2) The point m moves on the function image in (1). Is there a point m that makes AM⊥BM? If it exists, find the coordinates of point m, if it does not exist, try to explain the reason.

Answers to quadratic function exercises in mathematics tutoring for the third grade.

_ _ _ _ _ _ _ _ Class name _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

First, multiple-choice questions:

1, quadratic function y=x2-( 12-k)x+ 12, when x >；; At 1, y increases with the increase of x, and when x

12(B) 1 1(C) 10(D)9

2, in the following four functions, y value decreases with the increase of x value is (b).

(A) (B) (C) (D)

3. If the image of quadratic function y=ax2+bx passes through point A (-1, 1), then ab has (d).

(a) Minimum value 0 (B) Maximum value 1 (C) Maximum value 2 (D) has the minimum value.

4. The image of parabola y=ax2+bx+c is as shown in the figure, OA=OC, then (a)

(a) AC+1= b (b) AB+1= c (c) BC+1= A (d) None of the above.

5. If the vertex of the quadratic function y=ax2+bx+c is in the first quadrant and passes through points (0, 1) and (-1, 0), then the range of S=a+b+c is (a).

0 & ltS & lt2(B)S & gt； 1 (C) 1<S & lt2(D)- 1 & lt； S & lt 1

6. If the distance from the vertex of the parabola y=x2-6x+c-2 to the X axis is 3, then the value of c is equal to (c).

(A)8 (B) 14 (C)8 or 14 (D)-8 or-14.

7. Translate the image of quadratic function by 2 units to the left, and then translate it by 1 unit upward, and the corresponding quadratic function relationship of the obtained image is (d).

(A) (B) (C) (D)

8.(3) If the parabola y=ax2+bx is known, when a >; 0, b<0, whose image passes (b)

A. Quadrants one, two and three B. Quadrants one, two and four

C. quadrants one, three and four d. Quadrants one, two, three and four

9. If yes, the vertex of the image of the quadratic function is in (d).

(a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant

10, known quadratic function, constant, when y reaches the minimum value, the value of x is (b).

(A) (B) (C) (D)

1 1, when a>0, b<0, c>0, the following image may be a parabola y=ax2+bx+c (a).

12. No matter what the value of x is, the condition that the value of function y=ax2+bx+c(a≠0) is always greater than 0 is ().

A.a & gt0，△& gt； 0b . a & gt； 0，△& lt； 0 C.a & lt0，△& lt； 0d . a & lt； 0，△& lt； 0]

Second, fill in the blanks:

13 As shown in the figure, it is known that the point M(p, q) is on the parabola y = x2- 1, the circle centered on m intersects the X axis at two points A and B, and the abscissas of the points A and B are two of the equations x2-2px+q = 0 about X, then the chord length AB is equal to. 2

14, let x, y and z satisfy the relation x- 1 = =, then the minimum value of x2+y2+z2 is. 59/ 14

On the image of 15 with known quadratic function y = ax2 (a ≥ 1), the abscissas of points A and B are-1 and 2 respectively, and point O is the coordinate origin. If △AOB is a right triangle, the circumference of △OAB is.

16, given that the abscissa of the intersection of the quadratic function y =-4x2-2mx+m2 and the inverse proportional function y = in the second quadrant is -2, then the value of m is. -7

17, the quadratic function is known. When x = _ _ _ _ _ _ _ the function reaches the minimum value. 2

18. There is a parabolic arch bridge with a maximum height of 16m and a span of 40m. Now put its schematic diagram in the plane rectangular coordinate system as shown in Figure (4), and the analytical formula for finding parabola is _ _ _ _ _ _ _ _ _ _ _ _. Y=0.04x2+ 1.6x

19 as shown in figure (5), A.B.C is three points on the image of quadratic function Y = AX2+BX+C (A ≠ 0). According to the positions of the three points given in the figure, A-0, C-0 and ⊿-0 can be obtained. (& lt、& lt、gt； )

20. The teacher gave a function. Four students, A, B, C and D, each pointed out a property of this function: A: The image of the function does not pass through the third quadrant.

B: The image of the function passes through the first quadrant. C: When x < 2, Y decreases with the increase of X. D: When x < 2, y > 0, we can see that these four students' statements are correct. Please construct a function _ _ _ _ _ _ _ _ _ _ _.

2 1, it is known that the image of the quadratic function y = x2+bx+c passes through the point a (c, 0) and is symmetrical about the straight line x=2, then the analytic formula of this quadratic function may be ————————— (just write a possible analytical formula).

22. The functional relationship between flying height h(m) and flying time t(s) is h = v0tsinα-5t2, where v0 is the initial launching speed of the shell and α is the launching angle of the shell. When v0=300 (), sinα= sinα =, and the maximum flying height of the projectile is _ _ _ _ _ _ _. 1125m

23, parabola y=-(x-L)(x-3-k)+L and parabola y=(x-3)2+4 are symmetrical about the origin, then l+k = _ _ _ _ _. -9

Third, answer questions:

23. It is known that the abscissas of the two intersections between the image of quadratic function Y = x2+bx+c and the X axis are x 1 and X2, respectively. The two real roots of quadratic equation X2+B2X+20 = 0 are x3 and x4, and X2-X3 = X 1-X4 = 3. Find the analytic expression sum of quadratic function

y=x2+3x+2 (-3/2，- 1/4)

24. In 2000, Shen Ying Automobile Refitting Factory of Dongfeng Company developed Type A agricultural vehicles with a cost of 20,000 yuan/vehicle, an ex-factory price of 24,000 yuan/vehicle and an annual sales price of 1 10,000 vehicles. In order to support the construction of ecological agriculture in the western development, the factory seized the opportunity of developing enterprises, comprehensively improved the scientific and technological content of type A agricultural vehicles, and raised the cost price of each agricultural vehicle.

(3) Find out the functional relationship between the annual profit Y (ten thousand yuan) and X from the sales of type A agricultural vehicles in this factory in 200 1 year.

(4) If the annual profit of selling Type A agricultural vehicles in 200 1 year reaches 40.28 million yuan, how many vehicles should be sold in that year?

y =- 1200 x2+400 x+4000 1 1400 10600

25. As the picture shows, there is a parabolic arch bridge. The width of AB under the bridge is 20m at normal water level. When the water level rises by 3 meters, it reaches the warning line CD. This is the water surface width of 10m. (1) Find the analytical formula of parabola in the coordinate system as shown in the figure.

(2) If the water level rises at the rate of 0.2m per hour when the flood comes, how many hours will it last from the warning line to the top of the arch bridge?

5 hours

26. When the car is running, it will slide forward for a certain distance after braking before stopping. We call this distance "braking distance", which is an important factor in analyzing accidents. On a curve with a speed limit of 40 b, two cars, A and B, walked in opposite directions and found that the situation was wrong. Brake at the same time, but still collided. Afterwards, the braking distance of a car was measured at the scene as 12m. The braking distance of car B is greater than 10m, but less than 20m. According to relevant data, the braking distance S A (m) of car A has the following relationship with the vehicle speed X (), where S A = 0. 1x+0.0 1x2. The relationship between the braking distance S B (m) of car B and the vehicle speed X () is shown in the following figure.

B car

27. Since the reform and opening up, a town has developed its local economy through multiple channels, with a gross national product of 200 million yuan in 1995. According to estimates, when the gross national product of this town is 500 million yuan, it can reach a well-off level.

(3) If 1996 starts, the town's gross national product will increase by 60 million yuan every year compared with the previous year, how many years will it take for the town to reach a well-off level? five

(4) Taking 200 1 as the first year, the town's gross national product in X year is Y billion yuan, and the relationship between Y and X is y= (x≥0). Can the town's GNP quadruple on the basis of 1995 (that is, reach four times the annual GNP 1995)? 2003

28. It is known that the quadratic function intersects the X axis at two points, that is, the point M (x 1, 0) n (x2, 0) and the Y axis intersect at the point h,

(1) If ∠HMO = 450∠MHN = 1050, ask: Resolution function;

(2) If, when point Q(b, c) is on a straight line, find the analytic expression of quadratic function. (y=-x2+ 1/3x+4/9 y=-x2-x)

29. it is known that the function y=-ax2+bx+c(a≠0) passes through the image points p (- 1, 2) and q (2, 4).

(1) proves that the intersection of parabolic image and X axis is on both sides of the origin, whether A is any real number or not; If its image has two intersections with the X axis, and A and B(A is on the left of B) intersect with the Y axis at point C, find the parabolic analytical formula;

(2) The point m moves on the function image in (1). Is there a point m that makes AM⊥BM? If it exists, find the coordinates of point m, if it does not exist, try to explain the reason.