# How do you find the vertex, axis of symmetry and intercepts of f(x)=x^2+3x+7?

Jan 16, 2018

Vertex $\left(- \frac{3}{2} , \frac{19}{4}\right)$

Axis of symmetry $x = - \frac{3}{2}$

#### Explanation:

Given -

$y = {x}^{2} + 3 x + 7$

Vertex
x coordinate of the vertex

$x = \frac{- b}{2} a = \frac{- 3}{2 \times 1} = - \frac{3}{2}$
y coordinate of the vertex
At $x = - \frac{3}{2}$
$y = {\left(- \frac{3}{2}\right)}^{2} + 3 \left(- \frac{3}{2}\right) + 7$
$y = \frac{9}{4} - \frac{9}{2} + 7 = \frac{9 - 18 + 28}{4} = \frac{19}{4}$

Vertex $\left(- \frac{3}{2} , \frac{19}{4}\right)$

Axis of symmetry $x = - \frac{3}{2}$