9-4 Using Transformations to Graph Quadratic Functions ...

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Students will use vertex form to graph quadratic equations and describe transformations from the parent function with 70% accuracy. Students will use vertex form to graph quadratic functions and describe the transformations from

thHeolptaMrecnDt ofuungcatiloAnlwgeitbhr7a02% accuracy.

9-4

Using Transformations to Graph Quadratic Functions

If a parabola opens upward, it has a lowest point. If a parabola opens downward, it has a highest point. This lowest or highest point is the vertex of the parabola.

The parent function f(x) = x2 has its vertex at the origin. You can identify the vertex of other quadratic functions by analyzing the function in vertex form.

The vertex form of a quadratic function is f(x) = a(x ? h)2 + k, where a, h, and k are constants.

Students will use vertex form to graph quadratic functions and describe the transformations from thHeolptaMrecnDt ofuungcatiloAnlwgeitbhr7a02% accuracy.

9-4

Using Transformations to Graph Quadratic Functions

y = a(x - h)2 + k

? `h' (a number is inside parenthesis)

? Addition: moves left Subtraction: moves right

? `k' (a number is outside parenthesis)

? Addition: moves up Subtraction: moves down

? `a'

? Vertical stretch/shrink ? If negative, graph is reflected over x-axis (flipped)

Students will use vertex form to graph quadratic functions and describe the transformations from thHeolptaMrecnDt ofuungcatiloAnlwgeitbhr7a02% accuracy.

9-4

Using Transformations to Graph Quadratic Functions

Students will use vertex form to graph quadratic functions and describe the transformations from thHeolptaMrecnDt ofuungcatiloAnlwgeitbhr7a02% accuracy.

9-4

Using Transformations to Graph Quadratic Functions

Because the vertex is translated h horizontal units and k vertical from the origin, the vertex of the parabola is at (h, k).

Helpful Hint

When the quadratic parent function f(x) = x2 is written in vertex form, y = a(x ? h)2 + k, a = 1, h = 0, and k = 0.

Students will use vertex form to graph quadratic functions and describe the transformations from thHeolptaMrecnDt ofuungcatiloAnlwgeitbhr7a02% accuracy.

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