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8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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Linear Functions
How to Graph using Slope, Y-int, X-int, Table,
Graphing Calc
How to Write Linear Equations
How to Graph Linear Inequalities
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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QUADRATIC FUNCTIONS
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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GRAPHING A QUADRATIC FUNCTION
A quadratic function has the form
y =ax2 +bx+c where a { 0.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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GRAPHING A QUADRATIC FUNCTION
The graph is U-shaped and is called
a parabola.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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GRAPHING A QUADRATIC FUNCTION
The highest or lowest point on the
parabola is called the vertex.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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GRAPHING A QUADRATIC FUNCTION
In general, the axis of symmetry for
the parabola is the vertical line
through the vertex.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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GRAPHING A QUADRATIC FUNCTION
These are the graphs of y =x2
and y =x2.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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GRAPHING A QUADRATIC FUNCTION
The origin is the vertex for both
graphs.
The origin is the lowest point on the
graph of y =x2, and the highest point
on the graph of y =x2
.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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GRAPHING A QUADRATIC FUNCTION
They-axis is the axis of symmetry
for both graphs.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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THE GRAPH OF A QUADRATIC FUNCTION
GRAPHING A QUADRATIC FUNCTION
CONCEPT
SUMMARY
The y-intercept is at (0, c).
The graph of y = ax2
+ bx + c is a parabola with these characteristics:
The parabola opens up ifa > 0 and opens down ifa < 0.The parabola is wider than the graph of y = x
2if a < 1 and
narrower than the graph y = x2
if a > 1.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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Graph y = 2x2 8x+ 6
SOLUTION
Note The y-intercept is (0, 6)
Since a >0, the parabola opens up.
Graphing a Quadratic Function
x y
-1 160 6
1 0
x y
2 -23 0
4 6
(0, 6)
(2,2)
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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(2,2)
Graphing a Quadratic Function
Graphgiven Vertex (2, -2) and y-intercept 6
Draw a parabola through the plottedpoints.
(0, 6) (4, 6)Plot the vertex.
Plot the y-intercept (0, 6) and its
symmetric point, (4, 6).
Draw the axis of symmetry x=2.
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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Finding the Vertex on TI83 if the
Parabola Opens Down Step 1: Graph the function
Step2: Press 2nd (yellow
button), CALC (above the
blue menu button TRACE)
Step 3: Select 4:
maximum. Press
ENTER. You will be back
at the graph screen.
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Finding the Vertex on TI83 if the
Parabola Opens Down Step4: You will be back at
the graph screen and will be
prompted for a left
bound. Move the cursor to apoint to the left of the
vertex. Then press ENTER.
Step 5: You will now be
prompted for a right
bound. Move the cursor to a
point to the right of the
vertex. Then press ENTER
8/8/2019 Graphing Quadratics Lesson (5.1),(5.2)
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Finding the Vertex on TI83 if the
Parabola Opens Down
Step6: You will be
prompted to guess where the
vertex is. Move the cursor to
a point as close as possible tothe vertex. Then press
ENTER.
Step 7: The answer will be
displayed at the bottom of
the screen. In this example,
the answer is (1.71, 542.86).