Edgenuity Quadratic Functions Complete Study Guide: Formulas, Solved Examples, and Faqs

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Pinpointing where the curve strikes the coordinate axes is central to passing the Edgenuity Algebra 1 unit test. Finding the y-intercept is direct: evaluate the function at x = 0, which always isolates the constant term c. If an equation reads y = -3x² + 5x - 7, the y-intercept sits at (0, -7).

Locating x-intercepts requires setting y = 0 and solving the resulting equation ax² + bx + c = 0. When simple factoring fails, apply the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Before executing the entire calculation, evaluate the radicand, known as the discriminant: D = b² - 4ac. This value tells you how many x-intercepts the graph possesses without forcing you to complete the entire radical operation:

If b² - 4ac > 0, the graph cuts through the x-axis twice, yielding two real solutions. If b² - 4ac = 0, the parabola vertex rests directly on the x-axis, creating exactly one real solution (a single double root). If b² - 4ac < 0, the parabola never touches the horizontal axis, producing zero real solutions and two complex roots. Recognizing this eliminates extensive manual work on conceptual questions asking only for the count of real roots.