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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 = ax2 + 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

image0.png

b is the y-intercept.

Example

Which of the following could be a graph of the function y = –x2 + 5x – 2?

(A)

image1.jpg

(B)    

image2.jpg

(C)    

image3.jpg

(D)    

image4.jpg

(E)    

image5.jpg

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).

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