Question

match each graph with its number of solutions. (1 point) two solutions one solution no solution

Explanation:

Step1: Analyze the first graph (top)

The top graph (parabola opening left) and the horizontal line: check intersections. The parabola and the line intersect at one point? Wait, no—wait, the first graph (top left - looking at the first plot) has the parabola and the line intersecting at one point? Wait, no, let's re - examine. Wait, the first graph (top) - the parabola and the horizontal line: how many times do they cross? Wait, the first graph (top) - the parabola and the line: maybe no solution? Wait, no, let's look again. Wait, the second graph (middle) - the parabola opening right, and the horizontal line: how many intersections? The middle graph: the parabola and the line intersect at two points? Wait, no, the third graph (bottom) - the parabola and the line: tangent? So one solution.

Wait, let's clarify:

• For a quadratic - like graph (parabola) and a horizontal line, the number of solutions (intersections) is determined by how many times they cross.

• First graph (top): The parabola and the line - do they intersect? If the parabola is opening left, and the line is horizontal. Let's see the coordinates. If the line is, say, y = 0 (the x - axis), and the parabola is opening left, maybe it touches at one point? Wait, no, maybe I got the graphs wrong. Wait, the problem is to match each graph with the number of solutions (two, one, no).

Let's re - identify:

• Graph 1 (top): Let's assume the top graph (first plot) - the parabola and the line: how many intersections? If the parabola and the line do not intersect (no solution), but that might not be. Wait, maybe:

• Graph 1 (top): two solutions? No, wait, the middle graph (second plot) - the parabola opening right, and the line: two intersections (two solutions). The bottom graph (third plot) - the parabola and the line are tangent (one solution). The top graph (first plot) - the parabola and the line: no intersection (no solution). Wait, that makes sense.

Wait, let's correct:

• Bottom graph (third one): The parabola and the line are tangent (touch at one point) → one solution.

• Middle graph (second one): The parabola and the line intersect at two points → two solutions.

• Top graph (first one): The parabola and the line do not intersect → no solution.

Step2: Match each graph

• Top graph (first) → no solution.

• Middle graph (second) → two solutions.

• Bottom graph (third) → one solution.

Answer:

Top graph (first) - no solution; Middle graph (second) - two solutions; Bottom graph (third) - one solution.

(If we consider the graphs as:

• First graph (top) → no solution

• Second graph (middle) → two solutions

• Third graph (bottom) → one solution)