# SAT Practice Questions: Graphing Quadratic Functions

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

**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*=*x*^{2}– 2*x*– 8

**C.***y*=*x*(*x*– 2) – 8

**D.***y*= (*x*– 1)^{2}– 9**The following drawing shows the graph of the equation***y*=*x*^{2}– 2*x*– 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

**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.)**The correct answer is Choice (B).**

The answer is a perfect square minus an integer. For the perfect square to produce*x*– 2*x*(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.