Chapter 8.3, Problem 2E

To determine

To Select: The right option which is not same as others and find the value for both.

Answer to Problem 2E

The last option is the different one.

The axis of symmetry is $x=2$

The maximum value of the function is 32.

Explanation of Solution

Given information: The quadratic function $f(x)=-2x^2+8x+24$ .

Formula used: x coordinate of vertex is $\frac{-b}{2a}$ Where ‘ b’ is coefficient of x term and ‘ a’ is coefficient of $x^2$ .

Calculation:

Let’s analyze each option.

When it says the maximum value of a function, it represents the y-coordinate of vertex which is ‘ k’ .

For open down parabola the greatest range is the y-coordinate of the vertex, which is ‘ k’

The third option direction says y-coordinate of vertex ‘ k’ .

The last option says the x coordinate of vertex ‘ h’ that would be our axis of symmetry.

So, last option is the different one.

Let’s find both answers.

x coordinate of vertex h = $\frac{-b}{2a}$

From the function

  $\begin{array}{l}a=-2\\ b=8\end{array}$

Plug in these values into the formula,

  $h=\frac{-8}{2(-2)}=2$

Substitute back x as 2 into f(x) which gives value for k .

  $f(2)=-2{(2)}^2+8(2)+24=32$

The axis of symmetry is $x=h$ . So, which is $x=2$ .

The maximum value of the function is 32.