Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the...

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Lesson 10-1 Graphing Quadratic Equations

Transcript of Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the...

Page 1: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

Lesson 10-1

Graphing Quadratic Equations

Page 2: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

Definitions

• Quadratic Function - can be written in the form of y = ax2 + bx + c, where a 0.

Parabola - The graph of a quadratic function is a parabola.

Page 3: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

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Parabola

positive

Negative

Page 4: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

Equation of the Axis of Symmetry

• The equation of the axis of symmetry for the graph of y = ax2 + bx + c, where c 0, is

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x =−b

2a

Page 5: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

6 Steps to Graphing Quadratic Equations

1. Solve for line of symmetry using

2. Plug x value into original equation to find vertex (x,y).

3. Define vertex as a minimum or a maximum.

4. Find value of three numbers above and below line of symmetry value.

5. Plot points you have found.

6. Draw graph.

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x =−b

2a

Page 6: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

Use a table of values to graph y = x2 - x - 2.

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x y

Page 7: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

Use a table of values to graph y = -2x2 + 2x + 4.

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x y

Page 8: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

Consider the graph of y = -2x2 -8x -2.

1. Write an equation of the axis of symmetry.

2. Find the coordinates of the vertex.

3. Identify the vertex as a maximum or a minimum.

4. Graph.

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x y

Page 9: Lesson 10-1 Graphing Quadratic Equations. Definitions Quadratic Function - can be written in the form of y = ax 2 + bx + c, where a 0. Parabola - The.

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x y


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Graphing Quadratic Functions A quadratic function is an equation of the form: y = ax 2 + bx + c.

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General Form of a Quadratic Equation y = ax 2 + bx + c.

General Form of a Quadratic Equation y = ax 2 + bx + c.

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