Investigating Graphs

of Quadratic Functions

Algebra I Honors Graphing Quadratic Functions Pankowski

Objectives

• You will be able to describe how the values of the coefficients of a quadratic function affect the graph.

• You will be able recognize the graph of a quadratic function by it’s equation.

Algebra I Honors Graphing Quadratic Functions Pankowski

ReviewHow to graph a quadratic function by hand:

1. Find the x-coordinate of the vertex: -b/(2a).2. Make a table of values, using x-values to the left and right of the vertex.3. Plot the points and connect them with a smooth curve to form a parabola.

Algebra I Honors Graphing Quadratic Functions Pankowski

Example:

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y = x 2 − 2x − 3a = 1b = -2c = -3

x-coordinate of vertex

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=−(−2) /(2*1)= 2 /2

=1

y-coordinate of vertex

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=12 − 2(1) − 3=1− 2 − 3

= −1− 3

= −4Vertex

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=(1,−4)

Algebra I Honors Graphing Quadratic Functions Pankowski

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y = x 2 − 2x − 3Pick values to left and right of Vertex (equidistant from vertex)

-Two units to the right and left of x=1 are x=3 and x=-1.

-The vertex is located at (1,-4).-One unit to the right and left of x=1 are x=0 and x=2.

-Make a table by substituting these x-values into your function to find their corresponding y-values.

Algebra I Honors Graphing Quadratic Functions Pankowski

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y = x 2 − 2x − 3

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x = 2

y = 22 − 2(2) − 3

y = 4 − 4 − 3

y = 0 − 3

y = −3

B = (2,−3)

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x =1

y =12 − 2(1) − 3

y =1− 2 − 3

y = −1− 3

y = −4

Vertex = (1,−4)

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x = 0

y = 02 − 2(0) − 3

y = 0 − 0 − 3

y = 0 − 3

y = −3

C = (0,−3)

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x = −1

y = (−1)2 − 2(−1) − 3

y =1− −2 − 3

y = 3− 3

y = 0

D = (−1,0)

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x = 3

y = 32 − 2(3) − 3

y = 9 − 6 − 3

y = 3− 3

y = 0

E = (3,0)

Algebra I Honors Graphing Quadratic Functions Pankowski

Table of Values

Point X Y

Vertex 1 -4

B 2 -3

C 0 -3

D -1 0

E 3 0

Algebra I Honors Graphing Quadratic Functions Pankowski

Plot the Points and Connect a Smooth Curve

Algebra I Honors Graphing Quadratic Functions Pankowski

Investigation

• Open your laptop

• Open the file on your desktop labeled “Multimedia1a_Dynamic_Worksheet_EHP.html”

• Answer the questions on the worksheet by investigating using the sliders