Solution: 1, intersection point: Let (x 1, 0) and (x2, 0) be the intersection points of the quadratic function and the X axis.

Then, you can set a quadratic function: y=a(x-x 1)(x-x2).

For example, it is known that the quadratic function intersects the X axis at (-1, 0) and (5,0) and passes through the point (4, 10). Find this quadratic resolution function.

Solution: Let the required quadratic function be y=a(x+ 1)(x-5), and substitute the point (4,-10) into y=a(x+ 1)(x-5).

Namely:-10 = a * 5 *( 1):a = 2.

Therefore, the quadratic function: y=2(x+ 1)(x-5) is: y=2x? -8x- 10

2. Vertex: Let the vertex of the quadratic function be (k, h).

Then, you can set a quadratic function: y=a(x-k)? +h

For example, if the vertex coordinate of the quadratic function is known as (-1, 5) and passes through the point (1, 1), then we can find the quadratic resolution function.

Solution: Let the quadratic function be: y=a(x+ 1)? +5 Substitute the point (1, 1) into y=a(x+ 1)? +5

Namely: 1=a*4+5, a=- 1.

So, the quadratic function: y=-(x+ 1)? +5 means: y=-x? -2x+4