Chapter 9.3, Problem 5CYU

To determine

To solve: The equation by examining the given graph of the related function.

Answer to Problem 5CYU

The equation of the graph is $y=2x^2+14x-16$ .

Explanation of Solution

Given information: The figure of graph is given.

Calculation: : The figure of graph is given.

The equation of intercept form of parabola is $y=a(x-m)(x-n)$ .

The graph has $x-$ intercept at $(-8,0)\mathrm{and}(1,0)$ .

So put $m=-8andn=1$ in intercept form of parabola.

  $\begin{array}{l}y=a(x-m)(x-n)\\ y=a(x-(-8))(x-1)\\ y=a(x+8)(x-1)\end{array}$

Parabola passes through the points $(0,-16)$ so put $x=0\mathrm{and}y=-16\mathrm{in}y=a(x+8)(x-1)$

  $\begin{array}{l}y=a(x+8)(x-1)\\ -16=a(0+8)(0-1)\\ -16=a(8)(-1)\\ -16=-8a\\ \frac{-16}{-8}=a\\ 2=a\end{array}$

Put $a=2\mathrm{in}y=a(x+8)(x-1)$ then:

  $\begin{array}{l}y=a(x+8)(x-1)\\ y=2(x+8)(x-1)\\ y=2(x^2-x+8x-8)\\ y=2(x^2+7x-8)\\ y=2x^2+14x-16\end{array}$

Thus, the equation of graph is $2x^2+14x-16$ .