Algebra 2 A
Chapter 5
Section 1
Graphing Quadratic Functions
Graphs of Quadratic Functions
• The shape of a quadratic graph is called a parabola.
• The axis of symmetry is the line that divides a parabola
into two mirror images.
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Graphs of Quadratic Functions
• The shape of a quadratic graph is called a
parabola.
• The axis of symmetry is the line that divides a
parabola into two mirror images.
• The vertex of a parabola is the point
where the parabola and the axis of
symmetry meet. It is the minimum or
maximum of the parabola. (It’s the
turning point.)
•Corresponding points are the mirror
images of points
Quadratic functions
y = ax2 + bx + c
1.) Look at a (leading coefficient of the quadratic):
If a is positive the parabola opens up
If a is negative the parabola opens down
2.) The axis of symmetry is at
x
3.)The vertex is at
b
2a
b
, yvertex
2a
to find the y coordinate in the vertex
plug in (-b/2a) and solve for y
4.) y-intercept is at (0, c)
5.)Minimum or Maximum value occurs at the vertex.
The min or max value is the y-coordinate of the vertex
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Example …..using algebra
Find the y-intercept point, and the line of symmetry
1.)
y = 3x2 + 6x – 1
Y-int pt ( 0, -1) the c remember!
x
b
2a
(6)
2(3)
x
1
So x = -1 is
the line of symmetry
2.) y = -3x2 – 4x
Y-int pt ( 0, 0)
So x = -2/3 is
the line of symmetry
Example using the previous work
Also find the vertex
1.) y = 3x2 + 6x – 1
Y-int pt ( 0, -1)
x = -1 is the line of symmetry
Put the x of the line of symmetry ( also the x coordinate of the vertex)
into the equation and find the y for the vertex
Vertex ( -1, -4)
2.) y = -3x2 – 4x
Y-int pt ( 0, 0)
x = -2/3 is the line of symmetry
Vertex ( -2/3, 4/3)
Vertex point:
b
, yvertex
2a
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Make a table that includes the vertex
on your calculator!!!
ex 2.) y = -3x2 – 4x
Y-int pt ( 0, 0)
x = -2/3 is the line of symmetry
Vertex ( -2/3, 4/3)
Knowing the line of symmetry give you a great place to start
just scroll up and down the table and see the points.
remember the vertex is on the line of symmetry so you
only need to really scoll up OR down.
Using the calculator to find the vertex
Like pg 240 example b
On the graph will help you find the vertex as well
try 2nd Calc max or min to help you find the vertex
QUADRATIC FUNCTIONS
Notice that the domain is all Real numbers
while the Range depends on whether the
function opens up or down.
Remember:
The a in y = ax2 + bx + c will tell you if it opens up or down
If the function opens down (a < 0), then the
range would start at the y coordinate for
the vertex and get smaller.
While if the function opens up (a> 0), then
the range would start at the y-coordinate of
the vertex and go up from there.
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When you graph quadratics in my class.
1.)
2.)
3.)
4.)
find the y-intercept
find the axis of symmetry
Find the vertex point.
Make a table with the vertex being in the
middle of your table.
5.) use the points from the table to graph the function.
(use a minimum of 5 points: vertex, y-intercept,
and the x-intercepts if the function has any)
In class example related to previous slide on the calculator
y = x2 – 2x + 1
1.)
2.)
3.)
4.)
find the y-intercept
find the axis of symmetry
Find the vertex point.
Make a table with the vertex being in the
middle of your table.
5.) use the points from the table to graph the function.
(use a minimum of 5 points: vertex, y-intercept,
and the x-intercepts if the function has any.)
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