# How do you find the axis of symmetry and vertex point of the function: y=3x^2 -8x +7?

Oct 1, 2015

Axis of Symmetry: $x = \frac{4}{3}$
Vertex: $\left(\frac{4}{3} , \frac{5}{3}\right)$

#### Explanation:

First, you will have to convert the equation into vertex form $y = a {\left(x - h\right)}^{2} + k$ by "completing the square". Afterwards, it will be easy to determine the axis of symmetry and the vertex:

Axis of Symmetry: $x = h$
Vertex: $\left(h , k\right)$

Solution
y=3x^2−8x+7
y-7=3x^2−8x
y-7=3(x^2−8/3x)
y-7+3(16/9)=3(x^2−8/3x+16/9)
y-7+16/3=3(x−4/3)^2
y-21/3+16/3=3(x−4/3)^2
y-5/3=3(x−4/3)^2
color(blue)(y=3(x−4/3)^2+5/3)

Axis of Symmetry
In the equation, $h = \frac{4}{3}$. Therefore the axis of symmetry is:
$x = h$
$\textcolor{red}{x = \frac{4}{3}}$

Vertex
In the equation, $h = \frac{4}{3}$ and $k = \frac{5}{3}$. Therefore, the vertex is:
$\left(h , k\right)$
color(red)((4/3,5/3)