Parabolas and Transformations

Learn and apply parabolas and transformations using equations, examples, and interpretation.

Lesson 1 of 53 parts Practice Flashcards

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Parent Function

Objective: Explain and use parent function in an Algebra 1 problem.

The graph y=x² is an upward-opening parabola with vertex (0,0), symmetric about the y-axis. Zero.

Worked examples

Try itExample 1.1: For y=(x−5)²+14, 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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Objective: Explain and use parent function in an Algebra 1 problem.

The graph y=x² is an upward-opening parabola with vertex (0,0), symmetric about the y-axis. Zero.

Worked examples

Try itExample 1.1: For y=(x−5)²+14, what is the vertex x-coordinate?Show answer

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

Objective: Explain and use horizontal and vertical shifts in an Algebra 1 problem.

In y=(x−h)²+k, the parent parabola shifts h units horizontally and k units vertically. The squared term becomes zero at x=h.

Worked examples

Try itExample 2.1: For y=(x−8)²+24, what is the vertex x-coordinate?Show answer

8. Vertex form reveals the horizontal coordinate where the square is zero. The answer is 8.

Objective: Explain and use stretch and reflection in an Algebra 1 problem.

In y=a(x−h)²+k, |a| controls vertical stretch and the sign of a controls opening direction. No, it changes opening direction.

Worked examples

Try itExample 3.1: For y=3(x−11)²+34, what is the axis x-coordinate?Show answer

11. The symmetry line goes through the vertex x-coordinate. The answer is 11.

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