Question

Let f(x)=`x^2`+2x-15. Determine the vaules of x for which f(x)=-16?

Answer 1

`x=-1`

Explanation:

Solve this quadratic equation by factoring since it is factorable.

Move everything to one side and make it equal to zero:

`x^2+2x+1=0`

Now you can factor:

`(x+1)^2` or
`(x+1)*(x+1)`

Now using the Zero Product Property,

`x+1=0`

The answer is `x=-1`

*If you want to learn about factoring, completing the square, or the quadratic formula, here are some links:
Factoring: https://www.khanacademy.org/math/algebra/quadratics/solving-quadratic-equations-by-factoring/v/example-1-solving-a-quadratic-equation-by-factoring, and https://www.khanacademy.org/math/algebra/quadratics/solving-quadratic-equations-by-factoring/a/solving-quadratic-equations-by-factoring

Completing the Square (Another method that works on most qudratic equations, also the basis of vertex form):
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-the-square/v/solving-quadratic-equations-by-completing-the-square, and
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-the-square/a/solving-quadratic-equations-by-completing-the-square

And the Quadratic Formula (This method works for any quadratic equation):
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/v/using-the-quadratic-formula, and
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/a/quadratic-formula-review
(The quadratic formula is given by `(-b+-sqrt(b^2-4ac))/(2a)` )