# October 10, 2012 - PowerPoint PPT Presentation

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October 10, 2012. Take out your graphing calculator. If at least 70% of students in the class have their graphing calculator in class today, we will do an activity with the calculator. If not, we will take notes on 5.2. Homework Questions?. PSAT Questions?. Graphing on TI-83/TI-84.

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October 10, 2012

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### October 10, 2012

• Take out your graphing calculator.

• If at least 70% of students in the class have their graphing calculator in class today, we will do an activity with the calculator.

• If not, we will take notes on 5.2.

### Graph using your calculator

• Graph each of the following using your graphing calculator, and sketch the graph on your paper.

## Graphing Parabolas

### Purpose

• Learn how to graph parabolas

### Outcome

• Graph parabolas

### Graphing Parabolas, Method 1

• Solve for the following:

• Axis of symmetry

• Vertex

• y-intercept (c)

• x-intercepts (also called the zeros or the roots)

• Draw a dashed line for the axis of symmetry

• Draw a point for:

• The vertex

• The y-intercept

• The reflection of the y-intercept

• The x-intercepts

• Sketch in the rest of the parabola

• Check that the shape agrees with the shape predicted by the sign of a

• a>0 (a is positive) opens up

• a<0 (a is negative) opens down

### Example 1: Graph

(-2)

Vertex = (-2, -1)

y-intercept = 3  (0, 3)

Reflection of y-intercept (-4, 3)

Solve for the roots/zeros/x-intercepts

### You-Try: Graph f(x) = 6 + x – x2

Axis of symmetry:

Vertex (from Warm-Up) = (.5, 6.25)

y-intercept = 6  (0, 6)

Reflection of y-intercept = (1, 6)

Solve for the roots/zeros/x-intercepts (from Warm-Up)

(-2, 0), (3, 0)

### Graphing Parabolas, Method 2

• Solve for the following:

• Axis of symmetry

• Vertex

• y-intercept (c)

• Draw a dashed line for the axis of symmetry

• Draw a point for:

• The vertex

• The y-intercept

• The x-intercepts

• The points with x-values ±1 and ±2 of the vertex

• Sketch in the rest of the parabola

• Check that the shape agrees with the shape predicted by the sign of a

• a>0 (a is positive) opens up

• a<0 (a is negative) opens down

### Vertex Form

• If has its vertex at (h, k), then it can be written in vertex form as

• This is similar to shifting absolute value equations.

### Example 3

• Given the graph of y = x2, graph the following:

• y = (x-3)2 + 5

• y = (x+1)2 + 3

• y = (x+4)2 – 7

### Assignment

• Parabola Graphing Worksheet

• Alternate Lesson

### Warm-Up: October 23, 2012

• Solve by factoring:

## Graphing Parabolas

### Essential Question

• How can we graph quadratic functions?

### Vertex

• The vertex is the minimum or maximum point of a parabola.

• The x-coordinate of the vertex is

• To find the y-coordinate, substitute the x value into the original equation.

• The vertex is a point, expressed as an ordered pair.

### Graphing Parabolas

• Find the vertex.

• Plot the vertex and draw a vertical dashed line to represent the axis of symmetry.

• Set up a T-table with the vertex in the middle.

• Choose 3 x-values on each side of the vertex.

• Find each y-value by substituting the x-value into the original equation.

• Plot your points.

• Connect the points with a smooth curve.

### Vertex Form

• If has its vertex at (h, k), then it can be written in vertex form as

• The graph will look like y=x2, but shifted to the right h units and shifted up k units.

### Example 3

• Given the graph of y = x2, graph the following:

• y = (x-3)2 + 5

• y = (x+1)2 + 3

• y = (x+4)2 – 7

### Assignment

• Parabola Graphing Worksheet