what do the following slides have in common?
TRANSCRIPT
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What do the following slides have in common?
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You’re thinking bridges, right?
Guess again!
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Architecture?
Still no!
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Motion
Throwing a ball Archery Catapult
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Satellite Dishes
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Any idea?
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Parabolas
Common architectural design. Common engineering design. Shows motion of a projectile. They just look cool.
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Chapter 6
Quadratic Equations
And
Functions
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Ax2 is the “quadratic term”. Bx is the “linear term”. C is the constant term.
cbxaxy 2
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Classify the following as quadratic, linear, or neither. Y=5x2-6
Y=3x-8
Y=4x3 + 2x2 -5x + 1
Y=-3x2
Quadratic
Linear
Neither
Quadratic
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What if the function isn’t in quadratic form? We will simplify it in order to put it into that
form!
7)5(4)( 2 xxf
7)2510(4 xx
7100404 2 xx
107404 2 xx
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Axis of Symmetry x = #
Vertex (h,k)
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Axis of Symmetry x = #
Vertex (h,k)
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Once you find the x-coordinate, plug that value into the function to find the matching y-coordinate.
Find the vertex.
a
bx
2
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y
x
X-intercepts (a.k.a. roots or zeros)
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Interesting things tend to happen at these locations. Vertex
X-intercepts
Axis of Symmetry
Highest or lowest point.
When an object hits the ground.
When an object changes direction.
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a= 2 and b = -8
x = 8/4, so x = 2.
y = 2(4)-8(2)+4, so y = -4.
The vertex is (2, -4).
482 2 xxy
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Find the x-intercepts.
Solve the quadratic equation using one of the following methods:
Graphing Factoring Completing the Square Quadratic Formula
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Ok, it will take a little time to cover all of those different methods. Focus on graphing. Let’s use calculators! Yes, the graphing kind.
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Graph. Hit 2nd, Calc. Choose the “Zero” option. Follow the commands.
482 2 xxy
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Your x-intercepts are:
(.59,0) and (3.41,0)
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What are the pro’s and con’s of this method? The calculator does all
of the work. The answer may be an
approximation. This may be more
difficult if your calculator cannot “see” the intercepts.
What if the intercepts are not real?
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More practice?
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