Question

The function f(x) is a quadratic function and the zeros of f(x) are −1 and 5. Assume the leading coefficient of f(x) is 1. Write the equation of the quadratic polynomial in standard form.

Answer 1

Explanation:

Zeros are solutions, are answers. So x = -1 and x = 5

What would've been the previous step to find that answer?

x + 1 = 0 would be where you'd get x = -1 from.

x - 5 = 0 would be where you'd get x = 5 from.

So the factors of this quadratic must've been:

(x + 1) and (x - 5)

Multiply these together.

(x + 1)(x - 5)

x^2 - 4x - 5

Since they were asking for an equation we ought to throw an = 0 on the end there, so you get

x^2 - 4x - 5 = 0

I like to think of this as a "working backwards" problem. Usually we get an equation, factor and solve it. This time we did all of that exactly in reverse order.