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2.1 Nonlinear Functions - Quadratic graphs and vertex form
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f of x equals, x squared, plus 4

The function f is defined as shown. Which of the following graphs in the xy-plane could be the graph of y equals, f of x ?

A.

​​​​​​​The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 8, negative 4, 4, and 8 are indied on each axis. There are horizontal gridlines at the numbers negative 8 through 8, in increments of 2, on the y axis, and there are vertical gridlines at the numbers negative 8 through 8, in increments of 2, on the x axis. The figure presents an upward opening parabola, whose vertex lies at negative 4 on the y axis. The parabola crosses the x axis at negative 2 and 2.

 

B.

​​​​​​​​​​​​​The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 8, negative 4, 4, and 8 are indied on each axis. There are horizontal gridlines at the numbers negative 8 through 8, in increments of 2, on the y axis, and there are vertical gridlines at the numbers negative 8 through 8, in increments of 2, on the x axis. The figure presents an upward opening parabola, whose vertex lies at negative 4 on the x axis. The parabola passes through the point with coordinates negative 6 comma 4, and the point with coordinates negative 2 comma 4.

 

C.

​​​​​​​The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 8, negative 4, 4, and 8 are indied on each axis. There are horizontal gridlines at the numbers negative 8 through 8, in increments of 2, on the y axis, and there are vertical gridlines at the numbers negative 8 through 8, in increments of 2, on the x axis. The figure presents an upward opening parabola, whose vertex lies at 4 on the x axis. The parabola passes through the point with coordinates 2 comma 4, and the point with coordinates 6 comma 4.

 

D.

​​​​​​​The answer choice presents the graph of a curve in the x y plane, with the origin labeled O. The numbers negative 8, negative 4, 4, and 8 are indied on each axis. There are horizontal gridlines at the numbers negative 8 through 8, in increments of 2, on the y axis, and there are vertical gridlines at the numbers negative 8 through 8, in increments of 2, on the x axis. The figure presents an upward opening parabola, whose vertex lies at 4 on the y axis. The parabola passes through the point with coordinates negative 2 comma 8, and the point with coordinates 2 comma 8.

 

The function f is defined as shown. Which of the following graphs in the xy -plane

Medium-difficulty · SAT Math · Nonlinear Functions — Quadratic graphs and vertex form. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice D is correct. For the quadratic function f of x equals, x squared, plus 4, the vertex of the graph is the point with coordinates 0 comma 4, and because the x squared term is positive, the vertex is the minimum of the function. Choice D is the only option that meets these conditions.

Choices A, B, and C are incorrect. The vertex of each of these graphs doesn’t correspond to the minimum of the given function.

 

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