Question

water and laser show
at an outdoor shopping mall, there is a water display and a laser display that can be represented by a quadratic function.

• the function for the path of the water display is $f(x)=-\frac{1}{2}x^{2}+4x$ where $f(x)$ represents the height of the water in feet after $x$ seconds traveling in the display.
• the function for the path of the laser display is $g(x)=-\frac{1}{32}(x - 16)^{2}+18$ where $g(x)$ represents the height of the laser in feet after $x$ seconds traveling in the display.

which statement represents the height of the water after 3 seconds?
a $f(3)=7\frac{1}{2}$
b $f(7\frac{1}{2}) = 3$
c $f(3)=9\frac{3}{4}$
d $f(9\frac{3}{4})=3$

Explanation:

Step1: Identify the function for water display

The function for the height of the water is $f(x)=-\frac{1}{2}x^{2}+4x$.

Step2: Substitute $x = 3$

We need to find the height of the water after 3 seconds, so we substitute $x = 3$ into $f(x)$.
$f(3)=-\frac{1}{2}(3)^{2}+4\times3$.

Step3: Calculate the value

First, calculate $-\frac{1}{2}(3)^{2}=-\frac{9}{2}$, and $4\times3 = 12$.
Then $f(3)=-\frac{9}{2}+12=\frac{-9 + 24}{2}=\frac{15}{2}=7\frac{1}{2}$.

Answer:

A. $f(3)=7\frac{1}{2}$