Question 350·Easy·Math

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The graph shows the height $y$ , in feet, of the top of an arch above the ground at horizontal distance $x$ , in feet.

Which choice gives the width of the arch’s opening at ground level, in feet?

On a graph of height against horizontal distance, ground level means the height is $0$ . The points where the curve meets the horizontal axis are $x$ -intercepts. Read both horizontal positions, then subtract the left one from the right one to find the width. The right crossing alone gives a position, not a distance.

Hints

Hint 1
An $x$ -intercept is where a graph meets the horizontal axis, so its height is $0$ . Ground level has that height. Which two crossings mark the edges of the opening?
Hint 2
The ground-level ends have two $x$ -coordinates, or horizontal positions. Width is the distance between them, not either position alone. How do you find the distance between two positions on an axis?

Step-by-step

Read the ground-level crossings
Step 1
Locate ground level on the graph
No Desmos needed. The given graph already shows where the arch reaches the ground. Ground level means height $y=0$ , so look where the curve meets the horizontal axis. Each such point is an $x$ -intercept, a point on the graph with height $0$ .
Step 2
Read the two ends of the opening
The curve meets the horizontal axis at $(4,0)$ and $(16,0)$ . Their $x$ -coordinates give the opening’s left and right horizontal positions: $4$ feet and $16$ feet.
Step 3
Find the distance between the ends
Width is the distance between the two ends, not the position of either end. Subtract the left position from the right:
$16-4=12$
The arch’s opening is $12$ feet wide. Taking $16$ alone would give only the right end’s position. Choice B.

Question 350·Easy·Math

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