Chapter 4.8, Problem 48PPS

To determine

To Find: The quadratic equation of the given graph.

Answer to Problem 48PPS

  $y=-\frac{1}{4}{x}^2-4x+2$

Explanation of Solution

Given:

  

Formula Used:

  $y=a{\left(a-h\right)}^2+k$

Calculation:

  $\begin{array}{l}Let\\ h=-8\\ k=18\\ y=14\\ x=-4\\ y=a{\left(a-h\right)}^2+k\\ \Rightarrow 14=a{\left(-4-\left(-8\right)\right)}^2+18\\ \Rightarrow 14=16a+18\\ \Rightarrow a=\frac{14-18}{16}=\frac{-4}{16}\\ \Rightarrow a=-\frac{1}{4}\\ \text{Equation of graph is}\\ y=-\frac{1}{4}{\left(x+8\right)}^2+18\\ \Rightarrow y=-\frac{1}{4}\left(x^2+64+16x\right)+18\\ \Rightarrow y=-\frac{1}{4}{x}^2-4x+2\end{array}$

Conclusion:

Thus the equation of the given graph is $y=-\frac{1}{4}{x}^2-4x+2$ .