Question

Write an equation of a quadratic function that has x-intercepts -2 and -5.

Answer 1

We have to write an equation of a quadratic function that has x-intercepts -2 and -5. This is, a function that has two roots: -2, and -5.

For doing so, we remember that if a function has n roots, it can be written as:

$f(x)=(x-x_1)(x-x_2)_{}\ldots(x-x_n_{})$

In this case, replacing the roots we have, we obtain that a quadratic function that has x-intercepts -2 and -5 is:

$\begin{gathered} f(x)=(x-(-2))(x-(-5)) \\ f(x)=(x+2)(x+5) \end{gathered}$