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Question the-pa

2.1 Nonlinear Functions - Quadratic graphs and vertex form
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  • The parabola opens upward.
  • The vertex is at the point (2 comma negative 2).
  • The parabola passes through the following points:
    • (1 comma negative nine tenths)
    • (2 comma negative 2)
    • (3 comma negative nine tenths)

The graph shown will be translated up 4 units. Which of the following will be the resulting graph?

A.

  • The parabola opens upward.
  • The vertex is at the point (2 comma 2).
  • The parabola passes through the following points:
    • (1 comma StartFraction 31 Over 10 EndFraction)
    • (2 comma 2)
    • (3 comma StartFraction 31 Over 10 EndFraction)

B.

  • The parabola opens upward.
  • The vertex is at the point (2 comma negative 6).
  • The parabola passes through the following points:
    • (1 comma negative StartFraction 49 Over 10 EndFraction)
    • (2 comma negative 6)
    • (3 comma negative StartFraction 49 Over 10 EndFraction)

C.

  • The parabola opens upward.
  • The vertex is at the point (negative 2 comma negative 2).
  • The parabola passes through the following points:
    • (negative 3 comma negative nine tenths)
    • (negative 2 comma negative 2)
    • (negative 1 comma negative nine tenths)

D.

  • The parabola opens upward.
  • The vertex is at the point (6 comma negative 2).
  • The parabola passes through the following points:
    • (5 comma negative nine tenths)
    • (6 comma negative 2)
    • (7 comma negative nine tenths)

The parabola opens upward. The vertex is at the point (2 comma negative 2). The parabola

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 A is correct. When a graph is translated up 4 units, each point on the resulting graph is 4 units above the point on the original graph. In other words, the y-value of each point on the graph increases by 4 . The graph shown passes through the points 1,-1, 2,-2, and 3,-1. It follows that when the graph shown is translated up 4 units, the resulting graph will pass through the points 1,-1+4, 2,-2+4, and 3,-1+4. These points are 1,3, 2,2, and 3,3, respectively. Of the given choices, only the graph in choice A passes through the points 1,3, 2,2, and 3,3.

Choice B is incorrect. This is the result of translating the graph down, rather than up, 4 units.

Choice C is incorrect. This is the result of translating the graph left, rather than up, 4 units.

Choice D is incorrect. This is the result of translating the graph right, rather than up, 4 units.

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