# How do you identify the important parts of  y = 2x^2 - 10x - 1 to graph it?

Sep 29, 2015

Vertex $\left(\frac{5}{2} , \frac{23}{2}\right)$ and axis of symmetry is $x = \frac{5}{2}$

#### Explanation:

This is a quadratic function, hence it represents a parabola. Important parts to identify is its vertex and the axis of symmetry.

This is done by completing the square for x, as shown below:

$y = 2 \left({x}^{2} - 5 x\right) - 1$

$y = 2 \left({x}^{2} - 5 x + \frac{25}{4} - \frac{25}{4}\right) - 1$

$y = 2 {\left(x - \frac{5}{2}\right)}^{2} + \frac{25}{2} - 1$

$y = 2 {\left(x - \frac{5}{2}\right)}^{2} + \frac{23}{2}$

This gives vertex $\left(\frac{5}{2} , \frac{23}{2}\right)$ and axis of symmetry is $x = \frac{5}{2}$