# ACT Trick for Quadratics: How to Quickly Find the Vertex Location of a Parabola

To save time when graphing a quadratic function on the ACT Math test, you can quickly find the location of the vertex of the parabola in relation to the *y*-axis. Just use the following simple trick based on the variables *a* and *b* (in the terms *ax*^{2} and *bx*):

When the signs of

*a*and*b*are the same (either both positive or both negative), the graph shifts to the left. That is, the vertex of the parabola is to the left of the*y*-axis.When the signs of

*a*and*b*are different (one is positive and the other is negative), the graph shifts to the right. In this case, the vertex of the parabola is to the right of the*y*-axis.

A good mnemonic for remembering this rule is that the word *same* and the word *left* both have four letters.

### Example

A quadratic function *y* = *ax*^{2} + *bx* + *c* crosses the *x* axis at *x* = 4 and *x* = –2. Which of the following must be true?

At first glance, you may think this difficult question isn’t even answerable. A quick sketch shows you that a lot of different parabolas could fit this description:

The only thing you know for sure is that the parabola’s vertex is horizontally in the middle of these two points, so it’s somewhere on the line *x* = 1. Thus, the parabola (whatever it looks like) is shifted to the right, so *a* and *b* have different signs. So *a* does not equal *b*, making the correct answer Choice (C).