Quadratic Functions — Test

Question 25 • Mathematics I

Which graph represents the function f of x is equal to negative x squared plus 5 ?

Answer

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 8, 9), has a vertex at (negative 5, 0), and goes through (negative 2, 10).

Image with description On a coordinate plane, a parabola opens down. It goes through (negative 3, negative 4), has a vertex at (0, 5), and goes through (3, negative 4).

Image with description On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 9), has a vertex at (negative 5, 0), and goes through (negative 2, negative 9).

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 2, 9), has a vertex at (0, 5), and goes through (2, 9).

Explanation

The function f(x) = −x² + 5 has its vertex at (0, 5), and the negative coefficient on x² means the parabola opens downward. Substituting x = 3 gives f(3) = −9 + 5 = −4; by symmetry, f(−3) = −4 as well. Choice D has a vertex at (0, 5), opens down, and passes through (−3, −4) and (3, −4).

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