Question

label each quadratic function with the number of solutions it has.

Explanation:

Step1: Recall solution definition

The number of solutions (real roots) of a quadratic function \( y = ax^2 + bx + c \) is determined by the number of times its graph intersects the \( x \)-axis.

Step2: Analyze Graph 1

Graph 1 is a parabola opening upwards. It intersects the \( x \)-axis at two distinct points. So, it has 2 solutions.

Step3: Analyze Graph 2

Graph 2 is a parabola opening downwards. It touches the \( x \)-axis at exactly one point (the vertex lies on the \( x \)-axis). So, it has 1 solution.

Step4: Analyze Third Graph (bottom - left)

This parabola (opening upwards) does not intersect the \( x \)-axis (the vertex is above the \( x \)-axis and it opens upwards). So, it has 0 solutions.

Step5: Analyze Fourth Graph (bottom - right)

This parabola (opening upwards) intersects the \( x \)-axis at two distinct points. So, it has 2 solutions.

Answer:

• Graph 1: 2 solutions
• Graph 2: 1 solution
• Bottom - Left Graph: 0 solutions
• Bottom - Right Graph: 2 solutions