# ACT Trick for Quadratics: How to Quickly Find the *y*-Intercept of a Parabola

To save time when graphing a quadratic function on the ACT Math test, you can quickly find the location of the *y*-intersept of the parabola based on the sign of the variable *c*.

The variable *c* is the constant term of the quadratic equation,* **y* = *ax*^{2} + *bx* + *c*.

Keep the following rules in mind:

When

*c*is positive, the*y*-intercept is positive. In other words, the parabola intersects the*y*-axis above the origin.When

*c*is negative, the*y*-intercept is negative. That is, the parabola intersects the*y*-axis below the origin.

Warning: Be clear that in a quadratic function, *c* is the *y*-intercept. In contrast, in a linear function

*b* is the *y*-intercept.

### Example

Which of the following could be a graph of the function *y* = –*x*^{2} + 5*x* – 2?

(A)

(B)

(C)

(D)

(E)

In this equation, *c* = –2, so the *y*-intercept is below the *y*-axis. As a result, you can rule out Choices (C), (D), and (E). Additionally, *a* = –1, so the parabola is concave down. So you also can rule out Choice (A), which makes the correct answer Choice (B).