Vertex Form of Quadratics
A free Algebra II lesson from the “Transformations of Functions” unit, with a worked example and practice problems including step-by-step solutions.
Vertex form writes a quadratic as y = a(x - h)^2 + k. This form shows the vertex directly: (h, k). The vertex is the turning point of the parabola, so it gives the maximum or minimum value depending on whether the graph opens down or up. Vertex form matters because it makes transformations visible: h shifts the graph left or right, k shifts it up or down, and a changes width and direction. A common mistake is reading h with the wrong sign; in (x - h), the x-coordinate is h.
What you'll learn
- Read vertex form
- Identify maximum or minimum
- Use vertex form to graph
Worked example
Problem. Find the vertex of y = -2(x - 4)^2 + 7.
- Compare with y = a(x - h)^2 + k.
- h = 4 and k = 7.
- The vertex is (4, 7).
Answer: (4, 7)
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. The vertex of y = (x - 3)^2 + 5 is...
Choices: (3, 5) · (-3, 5) · (3, -5) · (-3, -5)
Show solution
- Vertex form gives (h, k).
Answer: (3, 5)
2. The vertex of y = (x + 6)^2 - 2 is...
Choices: (-6, -2) · (6, -2) · (-6, 2) · (6, 2)
Show solution
- x + 6 means h = -6.
Answer: (-6, -2)
3. Does y = -3(x - 1)^2 + 8 open up or down?
Choices: Down · Up · Left · Right
Show solution
- a is negative.
Answer: Down
4. For y = (x - 9)^2 - 4, what is the axis of symmetry?
Show solution
- The axis is x = h.
Answer: 9
5. For y = -2(x + 5)^2 + 11, the maximum value is...
Choices: 11 · -5 · 2 · -2
Show solution
- Opening down means the vertex y-value is the maximum.
Answer: 11
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