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5 1 Graphing Quadratic Functions(Day 1 )
Objective CA 10 Students graph quadratic
functions and determine the maxima, minima, and
zeros of the function.
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The graph of a quadratic function is U shaped
and is called a parabola.
The graph of y x2 and y - x2 are shown.
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The origin is at the bottom of the graph y x2
and the highest point of the graph y - x2.
The lowest or highest point on the graph of a
quadratic function is called the vertex.
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The graphs of y x2 and y - x2 are symmetric
about the y axis, called the axis of
symmetry.
In general, the axis of symmetry for the graph is
the vertical line through the vertex.
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Quadratic functions have 3 forms
1. A quadratic function has the form (standard
form)
where a ? 0.
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The graph of a quadratic function
is a parabola with these characteristics

• The parabola opens up if a gt 0 and opens down if
  a lt 0.

• The parabola is wider than the graph of y x2
  if a lt 1 and narrower than the graph of y x2
  if a gt 1

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(characteristics continued)
The x-coordinate of the vertex is
The axis of symmetry is the vertical line
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2.

• Characteristics of graph
• The vertex is (h, k)
• The axis of symmetry is x h

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3.

• Characteristics of graph
• The x intercepts are p and q.
• The axis of symmetry is halfway between (p, 0)
  and (q, 0).

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Example 1 Graphing a Quadratic Function.
Graph
1. Coefficients for this function are
a 2
b -8
c 6
2. Since a gt 0 the parabola opens upward.
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3. Find and plot the vertex.
The y - coordinate is
Vertex (2, -2)
So the vertex is (2, -2)
Draw the axis of symmetry x 2
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4. Draw the axis of symmetry x 2
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Plot two points on one side of the axis of
symmetry, such as (1, 0) and (0, 6).
Use symmetry to plot two more points such as (3,
0) and (4, 6).
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Draw the parabola through the points.
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Example 2 Graphing a Quadratic function in
Vertex from. Graph
What we know
graph opens downward because a lt 0.
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The vertex is (-3, 4)
The A.o.S is x - 3
(-3,4)
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Graphing a Quadratic function in Intercept form.
Graph
Intercept Form
From observation we know the following
The parabola opens downward
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The x intercepts occur at
(-2, 0) and (4, 0)
The axis of symmetry lies half way between 2 and
4 which is x 1
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Example 4 Write the quadratic function in
standard form.
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Write the quadratic function in standard form.
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Homework Page 253 17 19, 21 43 odd
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(No Transcript)
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Investigating Parabolas page 249 1. Use a
graphing calculator to graph each of these
functions in the same viewing windows
2. Repeat Step 1 for these functions
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3. What are the vertex and the axis of symmetry
of the graph of y ax2?
(0, 0) x 0

1. Describe the effect of a on the graph of y ax2?

The graph opens up if a gt 0, the graph opens down
if a lt 0.
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By observation we know the following about this
function.
this means that the graph opens downward because
a lt 0.
The vertex is (-3, 4). The axis of symmetry is x
- 3
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To graph the function plot the vertex (-3,
4). Draw the axis of symmetry x -3
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Plot two points to the right such as (-1, 2) and
(1, -4). Use the axis of symmetry to plot two
points to the left (-5, 2) and (-7, -4 )