Vertex and Axis

Learn and apply vertex and axis using equations, examples, and interpretation.

Lesson 2 of 53 parts Practice Flashcards

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Vertex

Objective: Explain and use vertex in an Algebra 1 problem.

The vertex is the turning point of a parabola and is (h,k) when the rule is a(x−h)²+k. The vertex y-coordinate.

Worked examples

Try itExample 1.1: For y=(x−5)²+15, what is the vertex x-coordinate?Show answer

5. Vertex form reveals the horizontal coordinate where the square is zero. The answer is 5.

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Vertex

Objective: Explain and use vertex in an Algebra 1 problem.

The vertex is the turning point of a parabola and is (h,k) when the rule is a(x−h)²+k. The vertex y-coordinate.

Worked examples

Try itExample 1.1: For y=(x−5)²+15, what is the vertex x-coordinate?Show answer

5. Vertex form reveals the horizontal coordinate where the square is zero. The answer is 5.

Axis of Symmetry

Objective: Explain and use axis of symmetry in an Algebra 1 problem.

The vertical line x=h passes through the vertex and pairs points at equal horizontal distances from it. Yes, for equal offsets from h.

Worked examples

Try itExample 2.1: For y=3(x−8)²+25, what is the axis x-coordinate?Show answer

8. The symmetry line goes through the vertex x-coordinate. The answer is 8.

Minimum and Maximum

Objective: Explain and use minimum and maximum in an Algebra 1 problem.

A positive leading coefficient gives a minimum at the vertex; a negative one gives a maximum over all real inputs. A restricted input interval can change the contextual extremum.

Worked examples

Try itExample 3.1: For y=(x−11)²+35, what is the minimum y-value?Show answer

35. A nonnegative square has minimum zero; add the vertical shift. The answer is 35.

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