Write a quadratic function whose graph has the given characteristics x-intercepts: -4,2 point on graph (0,-9)

y = (9/8)(x +4)(x -2)

When the x-intercepts are "a" and "b", you know factors of the function are (x-a) and (x-b). So, we can write the function as ...

... y = k(x -(-4))(x -2) = k(x +4)(x -2) . . . . . for some scale factor k

We can find k using the given point.

... -9 = k(0 +4)(0 -2) = -8k

Dividing by -8 gives ...

... 9/8 = k

The desired function is ...

... y = (9/8)(x +4)(x -2)

... = (9/8)(x² +2x -8)

Sample Response: First, combine like terms by combining the variables and constants. Then use properties of equality to isolate the variable and find the value for x.

Step-by-step explanation: