First, multiple-choice questions (3 points for each question, ***30 points)

1. Among the following relationships, the one that belongs to the quadratic function (x is the independent variable) is ().

1

A.y =πx B. y =2x C. y = D.y =-x + 1

x

12

2. The parabola with the same opening direction as parabola y =-x is ().

2 12 12

A.y = x b . y =-x 2-x c . y = x+ 10d . y = x 2+2x-

542

2

3. Parabola y = (

The vertex of x -2) +3 is ()

A.(2，-3) B.( 1，4) C.(3，4) D. (2，3) 2

4. The parabola y=x moves left by 3 units and then moves down by 2 units, and the parabola expression is 2222.

a . y =(x-3)-2 b . y =(x-3)+2 c . y =(x+3)-2d . y =(x+3)+2 5。 Under certain conditions, if the relationship between the distance S (m) and the time T (sec) of an object is S =.

From 28 to 48 A.D.

6. The minimum value of quadratic function y =(x-1) +2 is () a.-2b.2c.- 1 7. The image of parabola y =x -mx -m+1 passes through the origin, so m is ().

a . 0 b . 1 c .- 1D . 1

22

8. It is known that the parabola y=ax+bx+c is shown in the right figure, so the root of the equation ax +bx+c=0 about x is A. There are two equal real roots B. There are two unequal positive real roots C. There are two real roots D. There is no real root 9. In the following quadratic function, the image of () does not intersect with the x axis.

a . y = 3xb . y = 2x-4c . y = x-3x+5d . y = x-x-2 10。 The approximate image of the quadratic function y =ax +bx +(c a ≠0) is shown in the figure.

The following statement is wrong ()

A. the function has the minimum value, b, the symmetry axis is a straight line, x = C, when x

2

2

2

2

2

2

2

2

22

1 2

1

Y decreases with the increase of x, when-1 < x < 2, Y > 0 2.

Iv. Answer questions (7 points for each question, ***2 1 point)

19. It is known that the vertex of the parabola is (1 2) and passes through point C (2 2,8). (1) Find the analytical formula of parabola; (2) find the parabola and y.

Coordinates of the intersection of axes.

20. It is known that the image of quadratic function consists of parabola y = 2x 2.

Translation to the right, when x = 1, y = 1.

(1) Find the analytic expression of this quadratic function; (2) When the value of x is in what range, y increases with the increase of x?

2 1. Known quadratic function y =? The image of x2+bx+c passes through two points, a (2 2,0) and b (0 0,6). (1) Find the analytic expression of this quadratic function. (2) Find the intersection of the quadratic function image and the X axis.

V. Answer questions (9 points for each question, 27 points for * * *)

22. As shown in the figure, the image of quadratic function intersects with the X axis at points A and B, and intersects with the Y axis at point C. Points C and D are quadratic function graphs.

A pair of symmetrical points on the image, the image of a linear function passes through point B and point D, (1) to find the coordinates of point D; (2) Find the expression of a linear function; (3) According to the image, write the range of X that makes the value of the linear function greater than the value of the quadratic function.

23. A company has developed a novel small household appliance, and the production cost of each piece is 18 yuan. According to market research and pricing,

40 yuan

For sale, 20 pieces can be sold every day. In order to increase the sales volume, the daily sales volume can be increased by 4 pieces for every price reduction of 2 yuan. On the premise of ensuring profit: (1) If the price of each item is reduced by X yuan and the profit of goods sold every day is Y yuan, please write the functional relationship between Y and X and find out the range of independent variable X; (2) When the price is reduced by several yuan, the daily profit is the largest? What is the maximum profit?

25. As shown in the figure, the quadratic function y=ax2.

+bx+c

Image sum

The x axis intersects at points a and b,

Where the coordinates of point A are (-1 0), the coordinates of point C are (0,5), another parabola passes through point (1 8), and m is its vertex.

(1) Find the analytical formula of parabola; (2) Find the coordinates of point B and point M; (3) Find the area of △MCB.

Quadratic function test questions (2)

10. Known inverse proportional function y =

k

x

The image of is in the second and fourth quadrants, then the image of the quadratic function y =2kx 2-x +k 2 is roughly () 1. Multiple choice questions: (3 points for each question, ***30 points)

1, parabola y =(x -2)2

The vertex coordinate of +3 is ()

A (-2，3) B(2，3) C(-2，-3) D(2，-3)

2. Parabola y =- 1

3x 2

+3x -2 has the same shape as y =ax 2, but the opening direction is opposite.

Fill in the blanks (3 points for each small question, ***2 1 point)

Then a =( )A-1 1. Given that the function y=(m+2)xm(m+ 1) is a quadratic function, then m = _ _ _ _ _ _ _ .3b3c-3d65438.

three

2. The symmetry axis of the quadratic function y=-x2-2x is X = _ _ _ _ _ _ _ _ _ _ _ _

3. If there are two points (3, -8) and (-5, -8) on the image of quadratic function y = x 2+bx+c, then the symmetry axis of this parabola is () 3. The function s=2t-t2 has a maximum value when t = _ _ _ _ _ _ _ _ _. 4.

Given that the abscissa of the intersection of the parabola y=ax2+x+c and the x axis is-1, then a+c = _ _ _ _ _ _ _.

4. The image of parabola y = x 2-MX-m 2+1passes through the origin, so m is () 5. The vertex of the parabola y=5x-5x2+m is on the X axis, so m = _ _ _ _ _ _ _ _ _ _ _ _ _

A .0

B. 1

C.- 1

6. It is known that the image of quadratic function y=x2-2x-3 intersects the X axis at two points A and B, and there is a point C on the parabola above the X axis, and

2

When the area of △ABC is equal to 10, the coordinates of point C are _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. 5. Formulating a quadratic function whose vertex is () 7 y =x -2x-1. Some images of the known parabola y=x2+bx+c are shown in the figure.

Answer. y =(x - 1) 2

B.y =(x- 1)2-2 c . y =(x+ 1)2+ 1D . y =(x+ 1)2

-2

Ruo y

6. known quadratic function y = ax 2

The image of +bx +c (a ≠0) is shown in the figure, and the following conclusions are given:

Third, answer questions.

① A+B+C0. 1。 (8 points) Given the following conditions, find the analytical formula of quadratic function. (1) passes through (1, 0), (0,2) and (2,3).

The serial number of all correct conclusions is ()

A.③④

B.②③ C. ①④

D.①②

7. Put the quadratic function y =-2 (x- 1) 2 on the rectangular coordinate plane.

The image of -2 moves left by 1 unit, and then moves up by 1 unit.

Its vertex is () A. (0 0,0) B. (1, -2) C. (0,-1)d .(2(-2,1)

(2) The intersection of the image and the X axis is (-1, 0), and the vertex is (1, 4).

8. 18. It is known that the image of function y=3x2-6x+k(k is a constant) passes through point A(0.85, y

1), B( 1. 1, y2), c (,y 3), and ().

(A) y 1y2 >y3(C)y3 & gt； y 1 & gt； y2(D)y 1 & gt； y3 & gtY22。 (8 points) Known straight line y =x -2 and parabola

y =ax 2

+bx +c intersect at points (2, m) and (n, 3), parabola 9. Function y =kx 2.

If the image of -6x +3 intersects the x axis, the range of k is ().

The symmetry axis of a straight line is the straight line X = 3. Find the analytical expression of this parabola.

Answer. K 0), and this

Two points are symmetrical about parabola, and find the value of m and the distance from point D to X axis.

(1) Find the analytical formula of parabola;

(2) The truck is 4.5m high and 2.4m wide. Can it go through the tunnel? (3) If there are two lanes in the tunnel and there is a 0.4m isolation belt in the middle of the tunnel for safety reasons, can freight trucks still pass through the tunnel?

Six (item 24, 9 points, item 25 10, *** 19 points)

24. As shown in the figure, the parabola y =-x 2+2x +3 intersects with the X axis at points A and B (point A is to the left of point B), and intersects with the Y axis at point C, with the vertex of d. 。

25. As shown, in the plane rectangular coordinate system, point A,

The coordinates of C are (-10) respectively, and point B is on the X axis. The image of the existing (0) quadratic function passes through three points A, B and C, and its symmetry axis is the straight line x = 1, and the point P is below the straight line BC.

C does not coincide), a moving point (points P and B, the parallel line of Y axis passing through point P intersects BC at point F. 。

(1) Write the coordinates of points A, B and C and the symmetry axis of parabola directly;

(2) Connecting BC, intersecting the parabola symmetry axis at point E, point P being the moving point on BC line, passing point P being PF∑DE intersecting parabola at point F, and the abscissa of point P being m; ① The length of the line segment PF is expressed by an algebraic expression containing m, and the quadrilateral is found when m is a value.

Is PEDF a parallelogram?

Let the area of △BCF be S, and find the functional relationship between S and M. 。

(1) Find the analytic expression of quadratic function;

(2) If the abscissa of point P is m, express the length of line segment PF with an algebraic expression containing m; (3) Find the maximum value of △PBC area and the coordinates of point P at this time.

(Question 25)