Chapter 9.1, Problem 69HP

To determine

To Find:

Whether Chase and Jade are correct or not. Explain.

Answer to Problem 69HP

Chase is wrong and Jade is correct.

Explanation of Solution

Given Information:

Chase and Jade are finding the axis of symmetry of a parabola.

  

Concept Used :

• Quadratic Functions:
• Quadratic functions are non-linear and are of the form:

$f(x)=a{x}^2+bx+c;a\ne 0$

This is the standard form of Quadratic function.

• Shape of the graph of a Quadratic function is called Parabola.
• Parabolas are symmetric about a central line called Axis Of Symmetry.
• The axis of symmetry intersects a parabola only at one point , called the Vertex.
• Axis of Symmetry: Passes through the vertex and divides the parabola into two congruent halves.

$x=-\frac{b}{2a}$

Calculation:

  $\begin{array}{l}Chase\\ y=-x^2-4x+6\\ x=-\frac{b}{2a}\\ x=-\frac{4}{2(-1)}\\ x=2\end{array}$   $\begin{array}{l}Jade\\ y=-x^2-4x+6\\ x=-\frac{b}{2a}\\ x=-\frac{-4}{2(-1)}\\ x=-2\end{array}$

We calculate the axis of symmetry for the equation :

  $y=-x^2-4x+6$

Comparing it with the standard form of quadratic equation $y=a{x}^2+bx+c$

We have , a = -1 ,b = -4 , c = 6

Axis of symmetry $x=-\frac{b}{2a}=-\frac{-4}{2(-1)}=-2$

So, Jade is correct.

Chase is wrong since he has taken b = 4 instead of -4.