Tips For Success

Some questions on standardized tests ask you to describe how changing an equation affects its graph. Read the sample question below. Then follow the tips to answer it.

TIP 1

You may want to sketch the graphs of both equations and compare the graphs.

How would the graph of y = x 2 − 1 y equals . x squared , minus 1  change if the equation became y = x 2 + 2 ? y equals , x squared , plus , 2 question mark

1. The graph would shift 3 units down.
2. The graph would shift 3 units up.
3. The graph would shift 2 units down.
4. The graph would shift 2 units up.

TIP 2

Think about what operation you would use to change y = x 2 − 1  to  y = x 2 + 2 . y equals , x squared , minus 1 , to , y equals , x squared , plus 2 .

Think It Through

To change the equation y = x 2 − 1 y equals . x squared , minus 1  to y = x 2 + 2 , y equals , x squared , plus , 2 comma  you add 3 to the expression x 2 − 1 : x squared , minus , 1 colon

y = x 2 − 1 + 3 = x 2 + 2 y equals . x squared , minus 1 plus . 3 equals . x squared , plus 2

Adding 3 to the constant term of a quadratic function causes the graph to shift 3 units up.

The correct answer is B.