Quadratics Checkpoint
A free College Algebra lesson from the “Quadratic Functions and Equations” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint mixes quadratic products, factoring, graph features, solving strategies, and applications.
What you'll learn
- Multiply and factor quadratics
- Solve quadratic equations
- Interpret quadratic graphs and applications
Worked example
Problem. Factor x^2 - 3x - 28.
- Find numbers that multiply to -28.
- -7 and 4 add to -3.
- Write (x - 7)(x + 4).
Answer: (x - 7)(x + 4)
Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Expand (x + 5)(x - 2).
Choices: x^2 + 3x - 10 · x^2 - 7x - 10 · x^2 + 10 · 2x + 3
Show solution
- The middle terms are -2x and 5x.
Answer: x^2 + 3x - 10
2. Factor x^2 + x - 30.
Choices: (x + 6)(x - 5) · (x - 6)(x + 5) · (x + 30)(x - 1) · (x + 3)(x - 10)
Show solution
- 6 and -5 add to 1.
Answer: (x + 6)(x - 5)
3. The vertex of y = (x + 1)^2 - 4 is...
Choices: (-1, -4) · (1, -4) · (-1, 4) · (1, 4)
Show solution
- Vertex form gives (h, k).
Answer: (-1, -4)
4. For h(t) = -t^2 + 8t, when does the maximum occur?
Show solution
- Halfway between zeros 0 and 8.
Answer: 4
5. Solve x^2 - 11x + 30 = 0.
Choices: x = 5 or x = 6 · x = -5 or x = -6 · x = 3 or x = 10 · No real solution
Show solution
- Factor as (x - 5)(x - 6).
Answer: x = 5 or x = 6
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