Chapter 1, Problem 13REAE

Solution

Sketch the graph of the function $y=-2{\left(x+8\right)}^2-3$ and label its vertex and axis of symmetry.

Given:

The function is $y=-2{\left(x+8\right)}^2-3$ .

Concept used:

The parabola in its standard form $y=a{\left(x-h\right)}^2+k\text{ where }a\ne 0$ has vertex $\left(h,k\right)$ and axis of symmetry is the line $x=h$ .

Graph:

The graph for the function $y=-2{\left(x+8\right)}^2-3$ in standard form of parabola is shown below.

  

Interpretation:

The graph for the function $y=-2{\left(x+8\right)}^2-3$ can be obtained by translating the graph of $y=-x^2$ , $8$ units towards left and $3$ units downwards. And comparing $y=-2{\left(x+8\right)}^2-3$ with the standard form of parabola, the vertex is $\left(-8,-3\right)$ and axis of symmetry is the line $x=-8$ as labelled in the graph.