Pg. 56 Homework

• Pg. 44 #72 – 74 all

• #27 Graph #29 Graph #31Graph

• #33 y = 3(x – 4)2 #35 y = 3x2 + 4 #37 No: y - int• #39 y = -2(x – 4)2 + 3 #54 (-3, -10); (-1, 2); (3, 2)• #55 f(x – 2) = |x – 2| #56 3f(x) = 3|x|• #57 2f(x + 3) – 1 = 2|x + 3| – 1• #58 12ft x 15ft #59 x = 3.5 ft #60 25ft x 25ft

1.5 Quadratic Functions and Geometric Transformations

Let f be the function given by the graph to the left.

• Determine the point on the graph of y = 3 + 2f(x – 1) corresponding to the following points:– > (-3, f(-3))– > (0, f(0))– > (2, f(2))– > (4, f(4))

1.5 Quadratic Functions and Geometric Transformations

Symmetry and Vertex• For the graph of the

function:

– The vertex is:

– The line of symmetry is:

• The Quadratic Formula is:

The Discriminant• The discriminant tells you

how many times the parabola will cross the x – axis.

• If…

2y ax bx c 2

,2 4

b bc

a a

x h

2 4

2

b b acx

a

2 4 0 2b ac solutions

2 4b ac

2 4 0 1b ac solution 2 4 0 0b ac solutions

1.5 Quadratic Functions and Geometric Transformations

• If 200 ft. of fence is used to enclose a rectangular plot of land using an existing wall as one side of the plot, find the dimensions of the rectangle with maximum enclosed area.

1.5 Quadratic Functions and Geometric Transformations

• A rectangle is 3 ft longer than it is wide. If each side is increased by 1 ft, the area of the new rectangle is 208 sq ft. Find the dimensions of the original rectangle.

1.5 Quadratic Functions and Geometric Transformations

• A rectangular pool with dimensions 25 by 40 ft is surrounded by a walk with a uniform width. If the area of the walk is 504 sq ft, find the width of the walk.

1.5 Quadratic Functions and Geometric Transformations

• Sally invests $20,000. She puts part of the money into an account that pays 4% annually, but she can withdraw from it without penalty, and she puts the rest into an account that pays 6% annually.– Write an equation that describes the total interest,

I, Sally receives at the end of 1 year in terms of the amount A invested at 6%.

– If Sally’s annual interest is $1086, how much of her original $20,000 did she invest at 6%?