Let’s think about what this image is showing.
It shows three different graphs, each with a parabola (the U-shaped curve) and a straight line. The title says “Linear-Quadratic Systems,” which means we’re looking at systems that have one linear equation (straight line) and one quadratic equation (parabola).
In math, when you solve a system of equations, you’re trying to find where the graphs intersect — because those points satisfy both equations at the same time.
Now let’s look at each graph:
1.
First graph (left): The line crosses the parabola in two places. That means there are two points where both equations are true → so,
two solutions.
2.
Second graph (middle): The line just touches the parabola at exactly one point. It doesn’t cross through — it’s tangent. So only one point satisfies both equations →
one solution.
3.
Third graph (right): The line and the parabola never meet. No intersection at all → so,
no solution.
This makes sense because depending on how the line is positioned relative to the parabola, they can intersect 0, 1, or 2 times.
You don’t need to do any calculations here — this is about understanding what the graphs represent visually.
Final Answer:
The image illustrates that a linear-quadratic system can have two solutions (if the line intersects the parabola twice), one solution (if the line is tangent to the parabola), or no solution (if the line and parabola do not intersect).
Parent Tip: Review the logic above to help your child master the concept of systems of linear and quadratic equations worksheet.
