Chapter 9.1, Problem 25P

Use a graphing calculator to graph each function. Identify the vertex and axis of symmetry.

$y=-2x^2+7$

To determine

To find the vertex and axis of symmetry for the given function.

Answer to Problem 25P

The vertex and axis of symmetry of the function $y=-2x^2+7$ is given by $\left(0,7\right)$ and $x=0$ .

Explanation of Solution

Given information:

The given function is $y=-2x^2+7$ .

Consider the given function $y=-2x^2+7$ .

The vertex of an up-down facing parabola of the form $y=a{x}^2+bx+c$ is given by $x_v=-\frac{b}{2a}$ .

Here, $a=-2;b=0;c=7$

  $x_v=-\frac{b}{2a}\Rightarrow x_v=-\frac{0}{2\times \left(-2\right)}=0$

  $y_v=7$

Therefore, the vertex of the parabola is $\left(0,7\right)$ .

Parabola is of the form $4p\left(y-k\right)={\left(x-h\right)}^2$ and is symmetric around the y-axis. Axis of symmetry is a line parallel to the y-axis which intersects the vertex at $x=0$ .

Therefore, the vertex and axis of symmetry of the function $y=-2x^2+7$ is given by $\left(0,7\right)$ and $x=0$ .