Chapter 9.2, Problem 4STP

For Exercises 1-5, choose the correct letter.

To determine

To choose the correct letter. Which graph represents the function.

Answer to Problem 4STP

The graph is,

  

the option is G.

Explanation of Solution

Given information: The function is, $y=3x^2+12x-6$ .

The option is,

F.

  

G.

  

H.

  

I.

  

Calculation: The solution is obtained as,

The graph of $y=a{x}^2+bx+c$ , where $a\ne 0$ , has the line $x=-\frac{b}{2a}$ as its axis of symmetry.

The x-coordinate of the vertex is $-\frac{b}{2a}$ ,

Because $a\succ 0$ , the parabola opens upward.

From the given, we have: $a=3\&b=12$ .

Axis of symmetry: $x=-\frac{12}{2\left(3\right)}=-2$

The x-coordinate of the vertex is -2. Solving for the y-coordinate,

  $y=3{\left(-2\right)}^2+12\left(-2\right)-6=-18$

So, the vertex is at $\left(-2,-18\right)$ .

Hence, the graph is,

  

The option is G.