Chapter 4.7, Problem 32PPS

To determine

To graph: the quadratic equation as mentioned in the problem.

Explanation of Solution

Given information:

The quadratic equation is $y=-\frac{5}{8}{\left(x-0\right)}^2-8$ .

Graph:

The graph mentioned below is in real number line of x axis and y axis.

Where vertex $V\left(0,-8\right)$ .

  

Interpretation:

Consider the quadratic equation $y=-\frac{5}{8}{\left(x-0\right)}^2-8$ .

The mentioned quadratic equation above is in vertex form $y=a{\left(x-h\right)}^2+k$ where $\left(h,k\right)$ is the vertex.

Therefore the vertex of equation is $\left(0,-8\right)$ .

We can write the mentioned quadratic equation in the standard form as $y=-\frac{5}{8}{x}^2+0x-8$ which is comparable to $a{x}^2+bx+c$ where $a=-\frac{5}{8}$ which is less than $0$ .

Since $a<0$ the direction of graph will be negative side of y axis.

The discriminant of standard form of quadratic equation $y=-\frac{5}{8}{x}^2+0x-8$ is $D=b^2-4*a*c\Rightarrow d={\left(0\right)}^2-4*\left(-\frac{5}{8}\right)*\left(-8\right)=0-20=-20$ .

Here also $D=-20<0$ .

Therefore the graph will lie below the x axis.

At $x=0$ the $y=-\frac{5}{8}{x}^2+0x-8$ will yield $y=-8$ .

Therefore graph will cut y axis at $\left(0,-8\right)$ .

Therefore the graph will be as mentioned below.