The graph of h(x) = −x2 − 10x + 5 can be used to model the height in feet of the curved support of an archway, where the x-axis represents the ground level and x represents the distance in feet at ground level from one side of an arch support to the other. Find the height of the highest point of the archway.

A. 15 ft
B. 25 ft
C. 30 ft
D. 20 ft

Answer would be greatly appreciated, added a few extra pts

Essentially looking for the maximum of the function h(x).
Assuming calculus is out of scope, you may use a simple formula -b/(2a) to find the x coordinate of the max point.
x = -b / (2a) = 10 / -2 = -5.

Plug in x=-5 into h(x) to find the height:
h(-5) = 30;

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ap8997154 ap8997154 · Answer 2 · 2022-06-03T10:59:51+02:00

A function assigns the values. The height of the highest point of the archway is 30ft.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The height of the arch is h(x)=-x²-10x+5, therefore, the highest point will be at,

dh/dx = -2x-10

substitute it with 0,

0=-2x-10

2x = -10

x = -5

Now, substitute the value of x in the equation to get the maximum height of the arch.

h(x) = −x² − 10x + 5

h(-5) = −(-5)² − 10(-5) + 5

h(-5) = -25 +50 +5

h(-5) = 30

Hence, the height of the highest point of the archway is 30ft.

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