Question

I NEED HELP!

The function f(x) is a quadratic function and the zeros of f(x) are - 2 and 5. The y-intercept of f(x) is 30. Write the equation of the quadratic polynomial in standard form.
f(x)=___________

Answer 1

Explanation:

First of all you have to put the zeros into factor form.

y1 = (x + 2)(x - 5)

Notice that the x changes sigh. You say that the zeros are -2 and 5. To get y1 to go to zero, you must make x the opposite sign of what you are given.

Now you have to expand the factored form to get the standard form

y = x^2 + 2x - 5x - 10

y = x^2 - 3x - 10

That's not the right answer.

f(0) = 30 but you have - 10 at the end so you have to multiply the factored form by - 3

-3(f(x)) = -3(x + 2)(x - 5)

-3(f(x)) = -3(x^2 - 3x - 10)

f(x) = -3x^2 + 9x + 30

f(0) = -3(0)^2 + 9(0) + 30

f(0) = 30

The quadratic still has roots of (x +2)(x - 5) but that 3 makes the y intercept = 30.

See the graph below.