Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a solving quadratic equations test PDF? Then this Algebra 1 test on Solving Quadratic Equations Four Ways checks the whole chapter, with points for each question. This test has 8 questions worth 20 points. Allow 45 minutes and work without notes. A calculator may be used for square roots. Show every step, because partial credit is given for correct setups and intermediate results.
Standards: A-REI.B.4a, A-REI.B.4b, A-APR.B.3, A-CED.A.1 · Level: Grade 9 Algebra 1
Question 2 Factoring (2 points)
Solve each equation.
- x² + 11x + 28 = 0 (1 point)
- 3x² − 12x = 0 (1 point)
Question 3 Complete the Square (3 points)
Solve x² + 10x + 7 = 0 by completing the square. Give exact answers and decimals rounded to the nearest hundredth.
Question 4 Quadratic Formula (3 points)
Solve 2x² − 3x − 7 = 0 with the quadratic formula. Round to the nearest hundredth.
Question 5 Discriminant (2 points)
Use the discriminant to decide how many real solutions each equation has.
- 3x² − 6x + 4 = 0 (1 point)
- x² + 6x + 9 = 0 (1 point)
Question 6 Garden Dimensions (3 points)
A rectangular garden is 7 feet longer than it is wide and has an area of 144 square feet. Find its width and length.
Question 7 When Does the Ball Land? (3 points)
The height of a ball is h(t) = −16t² + 24t + 16 feet after t seconds, as graphed.
- Write the equation that gives the landing time. (1 point)
- Solve it by factoring or by another method. (1 point)
- Say which solution makes sense and why. (1 point)
Question 8 Zero-Product Property (2 points)
Solve (2x − 5)(x + 8) = 0. Explain why each factor can be set equal to zero.
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