Chapter 8.4, Problem 31E

To determine

To calculate: The vertex and the axis of symmetry of the graph of the function $y=-6{\left(x+4\right)}^2-3$ .

Answer to Problem 31E

Vertex is $\left(-4,-3\right)$

Axis of symmetry is $x=-4$

For a quadratic function in standard form, $y=a{x}^2+bx+c$ , the axis of symmetry is a vertical line  $x=-\frac{b}{2a}$ and the vertex is point $\left(-\frac{b}{2a},y\left(-\frac{b}{2a}\right)\right)$ .

  

Now,

The graph of $y=-6{\left(x+4\right)}^2-3$ :

  

Thus,

Axis of symmetry is $x=-4$

Vertex is $\left(-4,-3\right)$

Explanation of Solution

For a quadratic function in standard form, $y=a{x}^2+bx+c$ , the axis of symmetry is a vertical line  $x=-\frac{b}{2a}$ and the vertex is point $\left(-\frac{b}{2a},y\left(-\frac{b}{2a}\right)\right)$ .

  

Now,

The graph of $y=-6{\left(x+4\right)}^2-3$ :

  

Thus,

Axis of symmetry is $x=-4$

Vertex is $\left(-4,-3\right)$