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. 2B. 10C. 20 D. 40

Answer: OPTION B.Step-by-step explanation: Given the function: [tex]f(x)= -2x^2 +20x[/tex] You can rewrite it with [tex]f(x)=y[/tex]. Then: [tex]y= -2x^2 +20x[/tex] Now, in order to solve for "x", you can follow this procedure: 1- Substitute [tex]y=0[/tex] into the function: [tex]0= -2x^2 +20x[/tex] 2- Factor the equation: [tex]0= -2x(x-10)[/tex] Therefore, you get: [tex]x_1=0\\\\x_2=10[/tex] This means that the distance between the two bases (in feet) of the arch is: [tex]d=10\ ft[/tex]