Answer:
C
Step-by-step explanation:
We can use the factored form of the quadratic equation, given by:
[tex]y=a(x-p)(x-q)[/tex]
Where a is the leading coefficient and p and q are the zeros.
We have zeros x = -2 and x = 3. So, let p = -2 and q = 3:
[tex]y=a(x+2)(x-3)[/tex]
Next, we are given that our y-intercept is (0, -30).
In other words, when x = 0, y = -30. So:
[tex]-30=a(0+2)(0-3)[/tex]
Solve for a:
[tex]-30=-6a\Rightarrow a=5[/tex]
Hence, our factored equation is:
[tex]\displaystyle y=5(x+2)(x-3)[/tex]
For the standard form, expand:
[tex]y=5(x^2-3x+2x-6)[/tex]
Simplify:
[tex]y=5(x^2-x-6)[/tex]
Distribute:
[tex]y=5x^2-5x-30[/tex]
Our answer is C.
