A system asks for one ordered pair that makes two equations true at the same time. On a graph, that pair is an intersection, a point shared by both graphs. For a line and a parabola, look for where they cross or touch, then click that point in Desmos. An axis crossing on only one graph won't work.
Hints
- Hint 1
An intersection is a point shared by two graphs. A point on only one graph satisfies only its equation, so which marked feature in the figure could satisfy both height equations?
- Hint 2
Type the two equations on separate Desmos lines and click where the graphs touch. An ordered pair lists first, in seconds after launch, and second, in meters above the ground.
Step-by-step
Find the shared point on the graph
Step 1Identify what makes a point a solution
The solid dot marks where the line touches the curve. That meeting spot is an intersection: a point on both graphs satisfies both equations. The line's -axis crossing is on the line but not the curve, so it can't be the solution.
- Step 2
Graph both height equations
Type and on separate Desmos lines. Desmos shows the line touching the curve at one point, matching the solid dot in the figure, so that's the point to click.
- Step 3
Read the time and height
Click the intersection; Desmos labels it . The first coordinate is time and the second is height, so the balloon is meters high at seconds. Choice A.