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Review of Chapter 5
Pre Calculus
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Things to Study• Difference between an inside change and an
outside change of a function– Inside Change affects the input(x)– Outside Change affects the output(y)
• Explaining Transformations– Through Graphs– Through Tables
• Quadratic Function– Vertex Form– Factor (Root) Form
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Transforming Points
• Given the point (2,5) on the graph of f(x), give a point of each transformation.
a)f(x-4)(6,5)
b)f(x) – 4(2,1)
c) f(4x)(.5,5)
d)4f(x)(2,20)
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Complete the TableX -3 -2 -1 0 1 2 3
f(x) -4 -1 2 3 0 -3 -6
f(-x)
f(x)-2
f(x-2)
2f(x)
f(x/2)
f(3x)
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Explain each Transformation from f(x) = 2x
a) f(-x) b) -f(-x) c) f(x) + 1.5 d) 5f(x)
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Write an Equation of the Quadratic Function Below
y = 3(x-2)2 or y = 3(x-2)(x-2)
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Creating Equations
• If you know a quadratic function has a root at -1 and a vertex at (1,4), find an equation that would represent the function
y = -1(x – 1)2 + 4
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Finding the Vertex
• Find the vertex of the following function.– Hint: Complete the Square…
v(t) = t2 + 11t - 4
Vertex: (-11/2, -137/4)(-5.5,-34.25)
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Quadratic Problem
• A ball is thrown into the air. Its height (in feet) t seconds after the throw is given by:
h(t) = 80t – 16t2
a)Interpret h(2)Height after 2 seconds is 96 feet
b)What is the ball maximum height traveled?(2.5, 100) 100 feet
c)When will the ball hit the ground?(5, 0) 5 seconds
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Explaining the Transformation