# How do you find the vertex and axis of symmetry for y = 4x^2 + 7?

Aug 15, 2015

The vertex is at $\left(x , y\right) = \left(0 , 7\right)$
The axis of symmetry is $x = 0$

#### Explanation:

The general vertex form for a quadratic is
$\textcolor{w h i t e}{\text{XXXX}}$$y = m {\left(x - a\right)}^{2} + b$
$\textcolor{w h i t e}{\text{XXXXXXXX}}$where the vertex is at $\left(a , b\right)$

$y = 4 {x}^{2} + 7$ can easily be transformed into vertex form as:
$\textcolor{w h i t e}{\text{XXXX}}$$y = 4 {\left(x - 0\right)}^{2} + 7$
$\textcolor{w h i t e}{\text{XXXXXXXX}}$where the vertex is at $\left(0 , 7\right)$

The equation is that of a parabola in standard position (opening upward), so the axis of symmetry is a vertical line through the vertex
i.e. $x = 0$