Question

47 which of the following graphs displays a quadratic relation that is not a function? a graph of a parabola opening downward with vertex at (0,7), crossing the x-axis at (-5,0) and (5,0)

Explanation:

Step1: Recall Vertical Line Test

A relation is a function if every vertical line intersects its graph at most once. For a quadratic relation (a parabola), if it opens horizontally (like \(x = ay^2 + by + c\)), it will fail the vertical line test. If it opens vertically (like \(y = ax^2 + bx + c\)), it passes the vertical line test.

Step2: Analyze Given Graph (Graph A)

The graph shown (Graph A) is a parabola opening downward (vertical opening, \(y = ax^2 + bx + c\) form). A vertical line drawn anywhere will intersect it at most once, so it is a function. But the question asks for a quadratic relation that is NOT a function. However, since only Graph A is shown here (and likely other graphs are missing, but assuming the correct graph is a horizontally opening parabola), the graph that is a quadratic relation (parabola) but not a function would be one opening horizontally (failing vertical line test). But based on the given Graph A, it is a function. If we assume there are other graphs (not shown here), the correct one would be the horizontally opening parabola (e.g., a graph of \(x = y^2\) - shaped parabola) which fails the vertical line test. But since only Graph A is provided, perhaps there was a mistake, but following the vertical line test: a quadratic relation not a function must be a horizontally opening parabola (fails vertical line test), while vertically opening (like Graph A) is a function.

Answer:

(Note: Since only Graph A is shown, but the question asks for a non - function quadratic relation, the correct graph would be a horizontally opening parabola (not shown here). If we assume the options include a horizontally opening parabola, that graph (e.g., if it's option B, C, or D not shown) would be the answer. But based on the given Graph A, it is a function. So likely the intended answer is a graph of a horizontally opening parabola (failing vertical line test).)