# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y= 1/20 x^2?

Jan 2, 2018

Axis of symmetry: $x = 0$ i.e the $y -$axis
${y}_{\min} = 0$

#### Explanation:

$y = \frac{1}{20} {x}^{2}$

The graph of $y$ is a parabola, of the form: $a {x}^{2} + b x + c$
Where: $a = \frac{1}{20} , b = c = 0$

The axis of symmetry of $y$ will occur where: $x = - \frac{b}{2 a}$

$\therefore$ Axis of symmetry is where: $x = 0$ i.e the $y -$axis

Since, $a > 0 \to y$ will have a minimum value

The minimum value of $y = {y}_{\min}$ will lie on the axis of symmetry.

Hence, ${y}_{\min} = \frac{1}{20} \cdot {0}^{2} = 0$

We can see these results from the graph of $y$ below:

graph{1/20x^2 [-10, 10, -5, 5]}