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Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

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, b^{2} - 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 I, Module 4, Lesson 15 (pdf)

Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

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, b

Lesson 15 Summary

You can use the sign of the discriminant, b^{2} - 4ac, to determine the number of real solutions to a quadratic equation in the form ax^{2} + 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. x^{2} - 2x + 1 = 0

2. 3b^{2} + 4b + 8 = 0

3. 2t^{2} + 7t - 4 = 0

4. q^{2} - 2q - 1 = 0

5. m^{2} - 4 = 3

**Exercises 6–10**

For Exercises 6–9, without solving, determine the number of real solutions for each quadratic equation.

6. p^{2} + 7p + 33 = 8 - 3p

7. 7x^{2} + 2x + 5 = 0

8. 2y^{2} + 10y = y^{2} + 4y - 3

9. 4z^{2} + 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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