Quadratic Functions — Test

Question 11 • Algebra I

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

Answer

Image with description A coordinate plane has both the x and y axes labeled from negative 10 to 10. A downward-opening parabola is plotted that passes through the point negative 3 comma negative 4, has a vertex at the point 0 comma 5, and passes through the point 3 comma negative 4.

Image with description A coordinate plane has both the x and y axes labeled from negative 10 to 10. A downward-opening parabola is plotted that passes through the point negative 6 comma negative 9, has a vertex at the point negative 5 comma 0, and passes through the point negative 2 comma negative 9.

Image with description A coordinate plane has both the x and y axes labeled from negative 10 to 10. An upward-opening parabola is plotted that passes through the point negative 2 comma 9, has a vertex at the point 0 comma 5, and passes through the point 2 comma 9.

Image with description A coordinate plane has both the x and y axes labeled from negative 10 to 10. An upward-opening parabola is plotted that passes through the point negative 8 comma 9, has a vertex at the point negative 5 comma 0, and passes through the point negative 2 comma 10.

Explanation

For f(x) = −x² + 5, the negative coefficient means the parabola opens downward. Its vertex is at (0, 5), and substituting x = 3 or x = −3 gives f(x) = −9 + 5 = −4. Choice A is the downward-opening graph with vertex (0, 5) that passes through (−3, −4) and (3, −4).

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