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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.

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:

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

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