Chapter 12.4, Problem 7MRE

To determine

To find: the vertex and the axis of symmetry of the graph of the given equation.

Answer to Problem 7MRE

The coordinate of the vertex is: $\left(0,0\right)$ .

The axis of symmetry is $x=0$ .

Explanation of Solution

Given information:

Given equation,

  $y=4x^2$

Concept used:

Vertex of parabola of the form $y=f\left(x\right)=a{x}^2+bx+c$ is given by

  $\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)$

The equation of axis of symmetry:

  $x=-\frac{b}{2a}$

Calculation:

Consider the given equation:

  $y=4x^2$

  $x$ Coordinate of the vertex:

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

To find out the $y$ coordinate, put $x=0$ in the given function:

  $\begin{array}{c}y=4{\left(0\right)}^2\\ =0\end{array}$

Hence, the coordinate of the vertex is: $\left(0,0\right)$

The equation of axis of symmetry:

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

Hence, the axis of symmetry is $x=0$ .