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Review

Find the first and second differences of the following:

This function is linear because the 2nd differences are 0

x	y
-2	-16
-1	-11
0	-6
1	-1
2	4

First Differences:
-11 - (-16) = 5
-6 - (-11) = 5
-1 - (-6) = 5
4 - (-1) = 5

Second Differences:
5 - 5 = 0
5 - 5 = 0
5 - 5 = 0

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Review

Find the first and second differences of the following:

This function is quadratic because the 2nd differences are constant.

x	y
-2	4
-1	1
0	0
1	1
2	4

First Differences:
1 - 4 = -3
0 - 1 = -1
1 - 0 = 1
4 - 1 = 3

Second Differences:
-1 - (-3) = 2
1 - (-1) = 2
3 - 1 = 2

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Review

Find the first and second differences of the following:

This function is quadratic because the 2nd differences are constant.

x	y
-2	0
-1	-3
0	-4
1	-3
2	0

First Differences:
-3
-1
1
3

Second Differences:
2
2
2

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Review

Find the first and second differences of the following:

This function is linear because the 2nd differences are 0.

x	y
-2	-4
-1	-3.5
0	-3
1	-2.5
2	2

First Differences:
0.5
0.5
0.5
0.5

Second Differences:
0
0
0

7 of 16

Review

Find the first and second differences of the following:

This function is quadratic because the 2nd differences are constant.

x	y
-2	1
-1	0
0	-3
1	-8
2	-15

First Differences:
-1
-3
-5
-7

Second Differences:
-2
-2
-2

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The Parabola

In yesterday’s activity we explored non-linear data:

Which we graphed...

… and drew a curve through

Some of you even found a link between using the first differences!

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The Parabola

But what if that was only half the story...

What happens when x is negative?

I present to you… (pause for dramatic effect)

The parabola!

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The Parabola

The curved, U or bowl shaped relation is called a parabola. They come in many sizes, but the same shape.

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Key Features

Since the shape is always the same, we have a few features we can identify of a parabola:

Term	Definition	How do I label it?
Vertex	The point at which a parabola changes between increasing and decreasing in value	(x, y)
Minimum/Maximum Value	The least or greatest value of a quadratic relation. It is the y-value of the vertex. A parabola can only have a max OR a min, not both.	y = #
Axis of Symmetry	A vertical line that passes through the vertex of a parabola. Represented by an equation “x = a” where a is the x-coordinate of the vertex.	x = #

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Key Features Continued

Since the shape is always the same, we have a few features we can identify of a parabola:

Term	Definition	How do I label it?
y-intercept	The y-coordinate of the point where the graph crosses the y-axis. The value of y when x = 0.	y = #
x-intercepts	The x-coordinates of the point or points where the graph crosses the x-axis. The value(s) of x when y = 0. There are 0, 1 or 2 of these	x = #, #
Zeros/Roots	The x-intercepts of a quadratic relation The value(s) of x when y = 0	x = #, #

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Find the Key Features From a Graph

Vertex: ( , )

Min/Max Value: __________

Axis of Symmetry:_________

y-Intercept:_________

x-Intercept(s):_________

Zeros/Roots:__________

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Find the Key Features From a Graph

Vertex: ( , )

Min/Max Value: __________

Axis of Symmetry:_________

y-Intercept:_________

x-Intercept(s):_________

Zeros/Roots:__________

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Find the Key Features From a Graph

Vertex: ( , )

Min/Max Value: __________

Axis of Symmetry:_________

y-Intercept:_________

x-Intercept(s):_________

Zeros/Roots:__________

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Find the Key Features From a Graph

Vertex: ( , )

Min/Max Value: __________

Axis of Symmetry:_________

y-Intercept:_________

x-Intercept(s):_________

Zeros/Roots:__________