Question

Please help asap I genuinely cannot figure this out

Find the equation of the parabola that has zeros of x = –2 and x = 3 and a y–intercept of (0,–30).


A) y = 5x2+ 5x – 30

B) y = –5x2 + 5x + 30

C) y = 5x2 – 5x – 30

D) y = x2 – 5x – 30

Answer 1

5,x6=5

4÷6=6

4=6=8

4=6687554=+÷976555££=6££6/=

Answer 2

C

Explanation:

We can use the factored form of the quadratic equation, given by:

`y=a(x-p)(x-q)`

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:

`y=a(x+2)(x-3)`

Next, we are given that our y-intercept is (0, -30).

In other words, when x = 0, y = -30. So:

`-30=a(0+2)(0-3)`

Solve for a:

`-30=-6a\Rightarrow a=5`

Hence, our factored equation is:

`\displaystyle y=5(x+2)(x-3)`

For the standard form, expand:

`y=5(x^2-3x+2x-6)`

Simplify:

`y=5(x^2-x-6)`

Distribute:

`y=5x^2-5x-30`

Our answer is C.