SAT Practice Questions: Graphing Quadratic Functions

By Ron Woldoff

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?
    sat1001-parabola
    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?
    sat1001-eqgraph
    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:
    SAT1001_eq2101
    The given equation ends with –3, not 1, so subtract 4: y = (x – 1)2 – 4.