Question

F(x) = x² - 4x − 21

Which of the following is an equivalent form of the function f above in which the zeros of f appears as constants or coefficients?

Answer 1

The factored form of the quadratic equation is y = (x - 7)*(x + 3). So the correct option is D.

How to rewrite the quadratic equation?

We want to rewrite the function:

f(x) = x² - 4x − 21

First we want to find the two zeros, to do so we need to use the quadratic formula. The zeros are given by:

`x = (4 \pm √(4^2 - 4*1*-21) )/(2*1) \\\\x = (4 \pm 10 )/(2)`

Then the zeros are:

x = (4 + 10)/2 = 7

x = (4 - 10)/2 = -3

Then we can write the factored form as:

y = (x - 7)*(x + 3)