Using the Quadratic Formula

Examples, solutions, and videos to help Algebra I students learn how to use the quadratic formula to solve quadratic equations that cannot be easily factored.
Students understand that the discriminant, b² - 4ac, , can be used to determine whether a quadratic equation has one, two, or no real solutions.

New York State Common Core Math Algebra I, Module 4, Lesson 15

Worksheets for Algebra 1

Lesson 15 Summary

You can use the sign of the discriminant, b² - 4ac, to determine the number of real solutions to a quadratic equation in the form ax² + bx + c = 0, where a ≠ 0.
If the equation has a positive discriminant, there are two real solutions.
A negative discriminant yields no real solutions and a discriminant equal to zero yields only one real solution.

Exercises 1–5
Solve the following equations using the quadratic formula.
1. x² - 2x + 1 = 0
2. 3b² + 4b + 8 = 0
3. 2t² + 7t - 4 = 0
4. q² - 2q - 1 = 0
5. m² - 4 = 3

Exercises 6–10
For Exercises 6–9, without solving, determine the number of real solutions for each quadratic equation.
6. p² + 7p + 33 = 8 - 3p
7. 7x² + 2x + 5 = 0
8. 2y² + 10y = y² + 4y - 3
9. 4z² + 9 = -4z

10. State whether the discriminant of each quadratic equation is positive, negative, or equal to zero on the line below the graph. Then identify which graph matches the discriminants below:

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