Chapter SH, Problem 9.9EP

To determine

To match the equation $y=\frac{1}{4}{x}^2$ with given graphs.

  

Answer to Problem 9.9EP

The graph of parabola equation $y=\frac{1}{4}{x}^2$ is graph B.

Explanation of Solution

Given information :

Given equation $y=\frac{1}{4}{x}^2$ and its one of the graph among the four graphs.

  

To find the correct graph for the equation $y=\frac{1}{4}{x}^2$ , determine the vertex of the parabola and the y -intercept of the graph.

Compare the given parabola equation with the standard form of the quadratic equation.

  $a=\frac{1}{4},b=0,c=0$

Write the equation for the axis of the symmetry.

  $x=\frac{-b}{2a}$

Substitute 0 for $b$ and $\frac{1}{4}$ for $a$ .

  $\begin{array}{c}x=-\frac{0}{2\left(\frac{1}{4}\right)}\\ =0\end{array}$

So, the equation for the axis of the symmetry is $x=0$ .

The vertex is equal to $\left(x,y\right)$ . To calculate the value of $y$ , substitute 0 for $x$ in the given equation.

  $\begin{array}{c}y=3{\left(0\right)}^2\\ =0\end{array}$

So, the vertex of the parabola is at $\left(0,0\right)$ .

The y -intercept of the graph of the equation is equal to the value of $c$ . So, the y -intercept of the graph of the equation is 0.

Draw the graph for the equation to verify.

  

Among the given graphs, the graph of parabola equation $y=\frac{1}{4}{x}^2$ is graph B.

Therefore, the graph of parabola equation $y=\frac{1}{4}{x}^2$ is graph B.