Chapter 7.5, Problem 2WE

To determine

To graph each given equation. Label the vertex and axis of symmetry. Find all intercepts.

Explanation of Solution

Given information :

Given equation $y=\frac{1}{3}{x}^2$

We know that the graph of the equation $y-k=a{\left(x-h\right)}^2$ opens upwards when $a>0$ and downwards when $a<0$ . Higher the values of $a$ , narrower the graph will be. Further if $h>0$ then the graph will slide to its right whereas it will shift on left side if the value of $h<0$ .

When $k>0$ the graph slides upwards and when $k<0$ then graph slides downwards.

Here the value of $a=\frac{1}{3}$ hence the graph opens downwards and center aligned as $k,h$ are zero.

Answer for given equation is,

  

Axis of symmetry is $x=0$

To find $x$ intercept we put $y=0$ we get,

  $x=0$