Question 1021·Easy·Math

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The graphs of the equations

y = 20

and

y = x^2 + 8x

in the $xy$ -plane intersect at the point $(x, y)$ . What is one possible value of $x$ ?

Two equations in $x$ and $y$ form a system of equations. Where their graphs cross, both equations are true. Graph each equation as written in Desmos, click the crossings, and read the first coordinate for $x$ . A graph's crossing of the $x$ -axis may not be a crossing of the other graph. Use a point shared by both graphs.

Hints

Hint 1
An intersection is a point on both graphs. One graph is the horizontal line $y=20$ , so what height must the curved graph reach at a shared point?
Hint 2
In an ordered pair $(x,y)$ , the first coordinate is $x$ . After you click a crossing in Desmos, which number in the displayed pair does the question ask for?

Step-by-step

Graph the two equations
Step 1
Connect a crossing to equal heights
At an intersection, both equations give the same height. The line says $y=20$ , so the curved graph must give $20$ at that $x$ :
$x^2+8x=20.$
Setting the curved graph equal to $0$ instead would find where it crosses the $x$ -axis, not where it crosses this line.
Step 2
Read a crossing's first coordinate
Type $y=20$ and $y=x^2+8x$ on separate lines in Desmos. Click both intersections: Desmos shows $(-10,20)$ and $(2,20)$ . The question asks for one possible value of $x$ , the first coordinate, so $x=2$ . Choice C.

Question 1021·Easy·Math

Strategy

Hints

Step-by-step

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Strategy

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Step-by-step

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