# What is the vertex form of y=-x^2+4x+1?

Jun 14, 2018

See explanation.

#### Explanation:

The vertex form of a quadratic function is:

where

and

where

## $\Delta = {b}^{2} - 4 a c$

In the given example we have:

$a = - 1$, $b = 4$, $c = 1$

So:

$p = \frac{- 4}{2 \cdot \left(- 1\right)} = 2$

$\Delta = {4}^{2} - 4 \cdot \left(- 1\right) \cdot 1 = 16 + 4 = 20$

$q = \frac{- 20}{- 4} = 5$

Finally the vertex form is: