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. Homework Questions?. PSAT Questions?. Graphing on TI-83/TI-84.

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October 10, 2012

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October 10 2012

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

Homework Questions?


Psat questions

PSAT Questions?


Graphing on ti 83 ti 84

Graphing on TI-83/TI-84


Graph using your calculator

Graph using your calculator

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


Warm up find the vertex roots and y intercept of f x x 2 4x 5

Warm-Up: Find the vertex, roots, and y-intercept of f(x) = x2 + 4x – 5


Due page 311 11 27 odd

Due: Page 311 #11-27 odd


Graphing parabolas

Graphing Parabolas


Purpose

Purpose

  • Learn how to graph parabolas


Outcome

Outcome

  • Graph parabolas


Graphing parabolas method 1

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

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 x 2

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

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

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

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

Assignment

  • Parabola Graphing Worksheet


October 10 2012

  • Alternate Lesson


Warm up october 23 2012

Warm-Up: October 23, 2012

  • Solve by factoring:


Homework questions1

Homework Questions?


Graphing parabolas1

Graphing Parabolas


Essential question

Essential Question

  • How can we graph quadratic functions?


Vertex

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 parabolas2

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.


Example 1 graph1

Example 1: Graph


You try 1 graph

You-Try #1: Graph


Vertex form1

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 31

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


Assignment1

Assignment

  • Parabola Graphing Worksheet


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