# How do you find the vertex and axis of symmetry, and then graph the parabola given by:  y = –x^2 + 4x + 2?

Oct 10, 2015

Vertex is $\left(2 , 6\right)$
Axis of symmetry $x = 2$

#### Explanation:

Given -

$y = - {x}^{2} + 4 x + 2$

Find Vertex

$x = \frac{- b}{2 a} = \frac{- 4}{2 \times - 1} = \frac{- 4}{- 2} = 2$

At $x = 2$

$y = - \left({2}^{2}\right) + 4 \left(2\right) + 2$
$y = - 4 + 8 + 2 = - 4 + 10 = 6$

Vertex is $\left(2 , 6\right)$
Axis of symmetry $x = 2$
Take two values on either side of $x = 2$. Find the corresponding $y$ values. Plot them in a graph sheet. Join them with a smooth curve.
x y

0 2
1 5
2 6
3 5
4 2

graph{-x^2+4x+2 [-14.23, 14.24, -7.12, 7.11]}
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