Chapter SH, Problem 9.11EP

To determine

To match the equation $y=2{\left(x-3\right)}^2$ with given graphs.

  

Answer to Problem 9.11EP

The graph of parabola equation $y=2{\left(x-3\right)}^2$ is graph C.

Explanation of Solution

Given information :

Given equation $y=2{\left(x-3\right)}^2$ and its one of the graph among the four graphs.

  

To find the correct graph for the equation $y=2{\left(x-3\right)}^2$ , determine the vertex of the parabola and the y -intercept of the graph.

Solve the equation.

  $\begin{array}{c}y=2{\left(x-3\right)}^2\\ =2\left(x^2-6x+9\right)\\ =2x^2-12x+18\end{array}$

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

  $a=2,b=-12,c=18$

Write the equation for the axis of the symmetry.

  $x=\frac{-b}{2a}$

Substitute $-12$ for $b$ and $2$ for $a$ .

  $\begin{array}{c}x=-\frac{\left(-12\right)}{2\left(2\right)}\\ =\frac{12}{4}\\ =3\end{array}$

So, the equation for the axis of the symmetry is $x=3$ .

The vertex is equal to $\left(x,y\right)$ . To calculate the value of $y$ , substitute $3$ for $x$ in the given equation.

  $\begin{array}{c}y=2{\left(3\right)}^2-12\left(3\right)+18\\ =18-36+18\\ =0\end{array}$

So, the vertex of the parabola is at $\left(3,0\right)$ .

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 $18$ .

Draw the graph for the equation to verify.

  

Among the given graphs, the graph of parabola equation $y=2{\left(x-3\right)}^2$ is graph C.

Therefore, the graph of parabola equation $y=2{\left(x-3\right)}^2$ is graph C.