Quadratic Deepening Checkpoint
A free Algebra II lesson from the “Transformations of Functions” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint reviews multiple quadratic strategies. The goal is to choose the method that fits the form and meaning of the problem.
What you'll learn
- Factor and solve quadratics
- Use vertex form and completing the square
- Use discriminants and applications
Worked example
Problem. Find the vertex of y = -3(x + 2)^2 + 5.
- Use vertex form y = a(x - h)^2 + k.
- x + 2 means h = -2.
- The vertex is (-2, 5).
Answer: (-2, 5)
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. Factor x^2 - 3x - 18.
Choices: (x - 6)(x + 3) · (x + 6)(x - 3) · (x - 9)(x + 2) · (x - 18)(x + 1)
Show solution
- -6 and 3 multiply to -18 and add to -3.
Answer: (x - 6)(x + 3)
2. Solve x^2 - 10x + 21 = 0.
Choices: 3 and 7 · -3 and -7 · 1 and 21 · 5 and 5
Show solution
- Factor as (x - 3)(x - 7).
Answer: 3 and 7
3. The vertex of y = 2(x - 5)^2 - 6 is...
Choices: (5, -6) · (-5, -6) · (5, 6) · (-5, 6)
Show solution
- Vertex form gives (h, k).
Answer: (5, -6)
4. What number completes the square for x^2 + 16x?
Show solution
- Half of 16 is 8.
- 8^2 = 64.
Answer: 64
5. Find the discriminant of x^2 - 2x - 15 = 0.
Show solution
- 4 - 4(1)(-15) = 64.
Answer: 64
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