Question

An arch $40$ feet in length and with a downward parabolic shape has a line drawn between the bases of its two legs . If the height above the ground, $y$, of the arch can be written as the function $y\left(x\right)=a(x-20)(x+20)$. Find the value of $a$ if $x$ represents the horizontal distance along the line between the bases from a point on the ground directly under the highest point of the arch.

• A. $-\frac{1}{40}$
• B. $-\frac{1}{20}$
• C. $-\frac{1}{10}$
• D. $-20$

Answer 1

The correct option is C $-\frac{1}{10}$

$y\left(x\right)=a(x-20)(x+20)$

Height of arch$=40ft$

According to given data,

at $x=0,y\left(x\right)=40$

$\therefore a(-20)\left(20\right)=40$

$\therefore a=\frac{-1}{10}$