Chapter 4.8, Problem 2CYU

To determine

To Find: Graph of the given inequality

Answer to Problem 2CYU

  $y>-11$

Explanation of Solution

Given:

  $y>x^2+6x-2$

Formula Used:

  $\frac{-b}{2a}\text{ to find }x\text{-coordinate of the vertex}$

Calculation:

  $\begin{array}{l}y>x^2+6x-2\left(1\right)\\ \Rightarrow \text{Using formula }\frac{-b}{2a}\text{ to find }x\text{-coordinate of the vertex}\text{.}\\ \Rightarrow \frac{-\left(6\right)}{2\times 1}=\frac{-6}{2}=-3\\ \Rightarrow x=-3\left(\text{put this value of }x\text{ in equation }1\right)\\ \Rightarrow y>{\left(-3\right)}^2+6\left(-3\right)-2\left(\text{using the value of }x\right)\left(2\right)\\ \Rightarrow y>-11\left(3\right)\end{array}$