# Question #74b68

Mar 30, 2017

Either factor or use quadratic formula. In this case, the zeros are $3$ and $- 2$.

#### Explanation:

Solving a quadratic function means to find the roots/zeros (same meaning, different word).

There are two ways to accomplish this:

1. Factor the equation (from standard to factored form).
2. Use the quadratic formula (in standard form).

Let's try factoring. Factoring is the fast and easier method of solving a quadratic function.

So first, let's find a common factor. In this case, I noticed that $8$ is common in all terms. So let's use that as our greatest common factor.

$f \left(x\right) = - 8 {x}^{2} + 8 x + 48$

$f \left(x\right) = - 8 \left({x}^{2} - x - 6\right)$

I took out the negative sign to make factoring much easier.

Now, we have a simple trinomial. So let's factor it normally: what two numbers added equals $b$ and multiplied, equals $a c$? In this case, it is $- 3$ and $2$.

$f \left(x\right) = - 8 \left(x - 3\right) \left(x + 2\right)$

And those are the zeros: $3$ and $- 2$.

If factoring did not work, we would have to use the quadratic formula and plug in the numbers from standard form.

Hope this helps :)