Question

Write a quadratic function whose graph has x intercepts of -6 and 3 and passes through (0,-9) Y=

Answer 1

We have the x-intercepts of the function x = -6 & x = 3, and the function passes y (0, -9).

We use the expression:

`f(x)=a(x-r_1)(x-r_2)`

Here a is a number, and r1 & r2 will be our x intercepts. So we replace them in the function:

`f(x)=a(x+4)(x-3)`

Since we have the y intercept given to us by the point (0, -9), we do as follows:

`f(0)=a(4)(-3)=-9\Rightarrow a=(3)/(4)`

So, we replace the values in our function:

`f(x)=(3)/(4)(x+4)(x-3)\Rightarrow f(x)=(3x^2)/(4)+(3x)/(4)-9`

So, that's our quadratic function that passes by (0, -9) and has x-intercepts at x = -6 & x = 3.

`y=(3x^2)/(4)+(3x)/(4)-9`