Question

ARCHITECTURE The curve of the archway under a bridge can be modeled by the equation $y=-\frac{1}{5}{x}^2+6x$, where $x$and $y$are measured in feet. Copy and complete the table for each value of $x$.

Short answer

$x$	$y$
0	0
10	40
15	45
20	40
30	0

Step-by-step solution

Step 1. Replace x with 0 and simplify.

Replace $x$with 0 in the given equation and simplify.

$$\begin{gathered} y=-\frac{1}{5}{\left(0\right)}^2+6\left(0\right) \\ =0 \end{gathered}$$

Step 2. Replace x with 10 and simplify.

Replace $x$with 10 in the given equation and simplify.

$$\begin{gathered} y=-\frac{1}{5}{\left(10\right)}^2+6\left(10\right) \\ =-20+60 \\ =40 \end{gathered}$$

Step 3. Replace x with 15 and simplify.

Replace $x$with 15 in the given equation and simplify.

$$\begin{gathered} y=-\frac{1}{5}{\left(15\right)}^2+6\left(15\right) \\ =-45+90 \\ =45 \end{gathered}$$

Step 4. Replace x with 20 and simplify.

Replace$x$ with 20 in the given equation and simplify.

$$\begin{gathered} y=-\frac{1}{5}{\left(20\right)}^2+6\left(20\right) \\ =-80+120 \\ =40 \end{gathered}$$

Step 5. Replace x with 30 and simplify.

Replace $x$with 30 in the given equation and simplify.

$$\begin{gathered} y=-\frac{1}{5}{\left(30\right)}^2+6\left(30\right) \\ =-180+180 \\ =0 \end{gathered}$$

Step 6. Make a table.

Make a table of obtained values of$y$ for every$x$ value.

$x$	$y$
0	0
10	40
15	45
20	40
30	0