Transformations and Modeling with Quadratics

Explore quadratic shift, feasible vertex, units in a model.

Lesson 2 of 53 parts Practice Flashcards

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Quadratic Shift

Objective: Explain quadratic shift and use it to solve or interpret a problem.

A rule a(x−h)²+k translates the parent curve and changes its vertical scale. Read h from the inside and k from the outside. The vertex output or vertical shift.

Worked examples

Try itTransformations and Modeling with Quadratics — practice 1.1: For y=2(x−5)²+6, find the vertex y-coordinate.Show answer

Step 1: The squared term is zero at x=5. Step 2: Then y=2(0)+6. Step 3: The vertex y-coordinate is 6.

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Quadratic Shift

Objective: Explain quadratic shift and use it to solve or interpret a problem.

A rule a(x−h)²+k translates the parent curve and changes its vertical scale. Read h from the inside and k from the outside. The vertex output or vertical shift.

Worked examples

Try itTransformations and Modeling with Quadratics — practice 1.1: For y=2(x−5)²+6, find the vertex y-coordinate.Show answer

Step 1: The squared term is zero at x=5. Step 2: Then y=2(0)+6. Step 3: The vertex y-coordinate is 6.

Feasible Vertex

Objective: Explain feasible vertex and use it to solve or interpret a problem.

The algebraic turning point is a contextual maximum or minimum only if its input lies inside the permitted domain. Otherwise check domain endpoints. A restricted interval may place its optimum at an edge.

Worked examples

Try itTransformations and Modeling with Quadratics — practice 2.1: For y=(x−8)²+7, find the minimum output.Show answer

Step 1: A square is at least zero. Step 2: At x=8, the square is zero. Step 3: The minimum output is 7.

Units in a Model

Objective: Explain units in a model and use it to solve or interpret a problem.

A vertex (time, height) has different units on each coordinate. Report the physical meaning and avoid extending a quadratic model past plausible conditions. Not when time starts at the launch event.

Worked examples

Try itTransformations and Modeling with Quadratics — practice 3.1: For y=4(x−11)²+3, find the vertex y-coordinate.Show answer

Step 1: The squared term is zero at x=11. Step 2: Then y=4(0)+3. Step 3: The vertex y-coordinate is 3.

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