Chapter 4, Problem 60SGR

To determine

To find: The quadratic function in vertex and direction.

Answer to Problem 60SGR

The direction of the equation is upward.

Explanation of Solution

Given information:

The given equation is $y=2x^2+12x-8$

Calculation:

Consider the equation $y=2x^2+12x-8$

The function of the equation in vertex form,.

  $\begin{array}{l}y=2x^2+12x-8\\ y=2\left(x^2+6x\right)-8\end{array}$

Add and subtract $6$ on the equation.

  $\begin{array}{l}y=2\left(x^2+6x+3\right)-8-6\\ y=2{\left(x+3\right)}^2-14\\ y=a{\left(x-h\right)}^2+k\end{array}$

Here $a=2,h=-3,k=-14$ thus the vertex is $\left(-3,-14\right)$ the axis of symmetry is $x=-3$ .

Plot the graph by using $TI-83$ calculator.

  

The trace and then graph to get the below output

  

The direction of opening of the equation is upward.

Therefore, the equation of the direction is is downward.