If you encounter a question with a graph of a parabola on the SAT Math exam, then you'll probably be dealing with a quadratic function. In the following practice questions, you'll need to find the forms of the equation that are equivalent to a given parabola.

Practice questions

  1. Which of the following equivalent forms of the equation shows the coordinates of the vertex of the parabola as constants in the equation?
    A. y = (x + 2)(x – 4) B. y = x2 – 2x – 8 C. y = x(x – 2) – 8 D. y = (x – 1)2 – 9
  2. The following drawing shows the graph of the equation y = x2 – 2x – 3. Which of the following equations is equivalent to the equation of the graph?
    A. y = (x – 1)2 + 4 B. y = (x – 1)2 – 4 C. y = (x + 1)2 + 4 D. y = (x + 1)2 – 4

Answers and explanations

  1. The correct answer is Choice (D). Per the drawing, the coordinates of the vertex of the parabola are (1, –9). Look for an equation containing 1 and –9. (In the answer, –1 contains a 1.)
  2. The correct answer is Choice (B). The answer is a perfect square minus an integer. For the perfect square to produce x – 2x (in the equation), it has to contain (x – 1)2. FOIL out the (x – 1)2 to see what the integer has to be:
    The given equation ends with –3, not 1, so subtract 4: y = (x – 1)2 – 4.

About This Article

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Ron Woldoff is the founder of National Test Prep, where he helps students prepare for the SAT, GMAT, and GRE. He is the author of several books, including GRE For Dummies and 1,001 GRE Practice Questions For Dummies.

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