Question

find an appropriate viewing window for the function, using the given x-values. then graph the function. find the coordinates of any turning points.
y = x² + 40, for x-values between -4 and 4.

choose the graph that uses the viewing window boundaries from above to show a complete graph of the function.
a.

b.

c.

d.

state whether the graph has a turning point in this window. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the graph has a turning point in this window. the turning point(s) is/are
(type an ordered pair. use a comma to separate answers as needed.)
b. there is no turning point.

Explanation:

Step1: Identify x-range

Given $x \in [-4, 4]$

Step2: Find y-values at endpoints

For $x=-4$: $y=(-4)^2 + 40 = 16 + 40 = 56$
For $x=4$: $y=(4)^2 + 40 = 16 + 40 = 56$

Step3: Find vertex (turning point)

For $y=ax^2+bx+c$, vertex at $x=-\frac{b}{2a}$. Here $a=1, b=0$, so $x=0$.
Substitute $x=0$: $y=0^2 + 40 = 40$.

Step4: Match to correct graph

The function is an upward-opening parabola with minimum at $(0,40)$, matching graph A.

Answer:

Graph Selection:

A. (The upward-opening parabola graph with lowest point at the center)

Turning Point:

A. The graph has a turning point in this window. The turning point(s) is/are $(0, 40)$