A system of equations asks for points that satisfy both rules. Graph each equation on its own Desmos line, then count their intersections. A fourth-degree curve can bend more than a parabola, so keep both its left and right sides in view. Counting only the crossings near the center can miss a solution.
Hints
- Hint 1
An intersection is a point on both graphs, so it satisfies both equations. Since the question asks how many points satisfy the system, what should you count on the graph?
- Hint 2
The term means the curve can have two dips, rather than the one dip of a parabola. Graph it in a window that shows both negative and positive -values before adding the line.
- Hint 3
Once both graphs are visible, follow the line across the entire curve, including its outer rising sections. Count where the graphs meet, not where either graph crosses an axis.
Step-by-step
Count intersections in Desmos
Step 1Identify what counts as a solution
A solution to a system is an point on both graphs. So you need to count their intersections, not the points where either graph meets an axis.
- Step 2
Show the curve's full shape
Type in Desmos. The graph has two dips with a high point between them. Don't treat it like a parabola, which has only one turning point; keep both sides in view.
- Step 3
Add the line and count shared points
Add on a second line. Click the four intersections: Desmos shows points near , , , and . Each is on both graphs, so exactly four points satisfy the system. Choice D.