Chapter 9.2, Problem 51PFA

a.

To determine

To find the value of a in the given function.

Answer to Problem 51PFA

Value of a is $a=0.0009$ .

Explanation of Solution

Given information :

The graph is given by the function $g\left(x\right)=0.0009{\left(x+7.05\right)}^2-0.071$ .

Function of a parabola in vertex form is given by the notation: $f\left(x\right)=a{\left(x-h\right)}^2+k$ .

The given function, $g\left(x\right)=0.0009{\left(x+7.05\right)}^2-0.071$ is already in this notation.

Hence a is represented by $a=0.0009$

b.

To determine

To find the value of h in the given function.

Answer to Problem 51PFA

Value of a is $h=7.05$ .

Explanation of Solution

Given information :

The graph is given by the function $g\left(x\right)=0.0009{\left(x+7.05\right)}^2-0.071$ .

Function of a parabola in vertex form is given by the notation: $f\left(x\right)=a{\left(x-h\right)}^2+k$ .

The given function, $g\left(x\right)=0.0009{\left(x+7.05\right)}^2-0.071$ is already in this notation.

Hence h is represented by $h=7.05$

c.

To determine

To find the value of k in the given function.

Answer to Problem 51PFA

Value of a is $k=-0.071$ .

Explanation of Solution

Given information :

The graph is given by the function $g\left(x\right)=0.0009{\left(x+7.05\right)}^2-0.071$ .

Function of a parabola in vertex form is given by the notation: $f\left(x\right)=a{\left(x-h\right)}^2+k$ .

The given function, $g\left(x\right)=0.0009{\left(x+7.05\right)}^2-0.071$ is already in this notation.

Hence h is represented by $k=-0.071$

d.

To determine

To select the options that are relating to the parent function of the graph.

Answer to Problem 51PFA

The options that are coherent with the given graph and the parent graph areC. stretched vertically, and E. translated left.

Explanation of Solution

Given information :

The parent graph function is $f\left(x\right)=x^2$ and given function is $g\left(x\right)=0.0009{\left(x+7.05\right)}^2-0.071$ .

Upon mapping both the given function and parent function as graph, the required options can be selected.

Hence the required options are C. stretched vertically, and E. translated left.