10 1 10 2 exploring quadratic graphs and functions
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10.1 & 10.2: Exploring Quadratic Graphs and Functions PowerPoint PPT Presentation


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10.1 & 10.2: Exploring Quadratic Graphs and Functions. Objective: To graph quadratic functions. Review:. Linear Equations? Quadratic Equations? Exponential Equations?. Activity:. Graph: y=x 2 and y=3x 2 on the same coordinate plane. How are they the same? How are they different?

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10.1 & 10.2: Exploring Quadratic Graphs and Functions

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10 1 10 2 exploring quadratic graphs and functions

10.1 & 10.2: Exploring Quadratic Graphs and Functions

Objective: To graph quadratic functions


Review

Review:

Linear Equations?

Quadratic Equations?

Exponential Equations?


Activity

Activity:

  • Graph: y=x2 and y=3x2 on the same coordinate plane.

  • How are they the same? How are they different?

  • Predict how the graph of y=1/3x2 will be similar and different to the graph of y=x2?


Vocabulary

Vocabulary:

  • Standard Form of a Quadratic Function = a function that can be written in the form of ax2+bx+c where a does not equal 0.

  • Quadratic Parent Function = f(x) = x2 or y = x2

  • Parabola: U-shaped curve = the graph of a quadratic function

  • Axis of Symmetry = The line that divides the parabola into 2 matching halves.

  • Vertex = The highest or lowest point of a parabola

  • Minimum/Maximum….


Anatomy of a parabola

Anatomy of a Parabola


Compare the widths of parabolas

Compare the widths of parabolas..

  • The larger the a…..?

  • The smaller the a….?


Graph

Graph:

  • Graph y=2x2 and y=2x2+3 and y=2x2-4 on a piece of graph paper.

  • What conclusion can you make about ‘c’?


More rules

More Rules:

  • Review: X = is a vertical or horizontal line?

  • Vertex of a parabola is the point…?

  • Axis of symmetry divides the parabola in half at what point?

  • Axis of symmetry of a quadratic function: x = -b/2a which is also the x-coordinate of the vertex.


Graph y ax 2 bx c

Graph y=ax2+bx+c

  • Graph the function -3x2+6x+5.

  • Step 1: Find the equation of the axis of symmetry and the coordinates of the vertex…


Graphing continued

Graphing continued…

  • Axis of symmetry = -6/2(-3) = 1

  • Plug in 1 for x and solve for the y-coordinate of the vertex.


Graphing continued1

Graphing continued:

  • Vertex = (1,8)

  • Axis of symmetry = x=1


Graphing continued2

Graphing Continued…

  • Find 2 other points on the graph.

  • 1. Use the y-intercept where x = 0.

  • When x=0, y=5

  • 2. Try another point on the same side of the vertex as the y-intercept… Let x = -1

  • When x=-1, y=-4 so another point is (-1, -4)


Graphing continued3

Graphing Continued…

  • Step 3: Reflect the points (0,5) and (-1, -4) across the axis of symmetry to get 2 more points… Draw the parabola.


Try your own

Try your own…

  • Graph f(x) = x2-6x+9


Recap conclusions

Recap: Conclusions

  • y=a2+bx+c

  • Positive a: opens up

  • Vertex = minimum

  • y=-a2+bx+c

  • Negative a: Opens down

  • Vertex = maximum

  • The larger the a, the narrower the graph.


Graphing quadratic inequalities

Graphing Quadratic Inequalities

  • Using the last equation: Graph –

  • y<x2-6x+9

  • Remember: dashed line; test one point below or above the line; then, shade.


Homework

Homework:

  • Practice 10-1 #1-18 and 10-2#4-15, 22-24


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