Chapter 2.2, Problem 67E

To determine

To calculate: Whether the axis of symmetry can be found using the points that lie on the graph of a quadratic function.

Answer to Problem 67E

The axis of symmetry cannot be determined.

Explanation of Solution

Given Information:

  $\left(2,3\right),\left(-4,2\right)$are the points that lie on the graph of a quadratic function.

Calculation:

A quadratic function can be written in standard form as,

  $y=a{x}^2+bx+c$

Substitute the two points and find the standard form of the parabola,

  $\begin{array}{l}y=a{x}^2+bx+c\\ 3=a{\left(2\right)}^2+b\left(2\right)+c\text{ Put }x=2,y=3\\ 3=4a+2b+c\mathrm{......}\text{ (1) Simplify}\\ 2=a{\left(-4\right)}^2+b\left(-4\right)+c\text{ Put }x=-4,y=2\\ 2=16a-4b+c\mathrm{......}\text{ (2) Simplify}\end{array}$

There are 2 equations and 3 variables are there. The values of $a,b,\text{ and }c$ cannot be found. Hence, the vertex of the parabola cannot be found.

Thus, the axis of symmetry cannot be determined.