# Find an equation for a polynomial of degree 2 with the following properties: Zeros: x=5 and x=-8F(0)=480?

### 3 Answers

Relevance

- PuzzlingLv 71 month agoFavorite Answer
Two zeros:

x = 5

x = -8

Rewrite those as equations equal zero:

x - 5 = 0

x + 8 = 0

Multiply the expressions together:

y = (x - 5)(x + 8)

But we can also multiply that by a constant 'a' and it doesn't change the zeros:

f(x) = a(x - 5)(x + 8)

Next we are told that f(0) = 480:

480 = a(0 - 5)(0 + 8)

480 = a(-5)(8)

480 = -40a

a = 480/-40

a = -12

So there's our final function:

f(x) = -12(x - 5)(x + 8)

If they want you to, you should expand that out:

f(x) = -12(x² + 8x - 5x - 40)

f(x) = -12(x² + 3x - 40)

Answer:

f(x) = -12x² - 36x + 480

Source(s): https://www.desmos.com/calculator/mcozoosk5g- Login to reply the answers

- Φ² = Φ+1Lv 71 month ago
y = (480/(5*-8))(x - 5)(x - 8) is an equation, as is y = -12x² + 156x - 480

Source(s): The parabola with non-zero x-intercepts: x₀, x₁, and non-zero y-intercept: y₀ is y = (y₀/(x₀ x₁))(x - x₀)(x - x₁).- Login to reply the answers

Still have questions? Get your answers by asking now.