Question

an architect designs an archway by resting the two bases of an arch on the floor. the shape of the arch can be modeled by the graph of the function f in the CY plane above. if f is defined by f(x)= -2x^2 +20 x where x is in feet what is the value of the distance d in feet between the two base of an arch? A. 2
B. 10
C. 20
D. 40

Answer 1

Answer: OPTION B.

Step-by-step explanation:

Given the function:

$f(x)= -2x^2 +20x$

You can rewrite it with $f(x)=y$. Then:

$y= -2x^2 +20x$

Now, in order to solve for "x", you can follow this procedure:

1- Substitute $y=0$ into the function:

$0= -2x^2 +20x$

2- Factor the equation:

$0= -2x(x-10)$

Therefore, you get:

$x_1=0\\\\x_2=10$

This means that the distance between the two bases (in feet) of the arch is:

$d=10\ ft$