October 10, 2012

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# October 10, 2012 - PowerPoint PPT Presentation

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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Presentation Transcript
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 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
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.