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 =…

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asked Sep 6, 2022 193k views

2 Answers

Mpjdem · Answer 1 · 2022-09-12T15:09:25+0000

Answer:

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.