CCA WK 24 Review

Vertex Form to Standard Form y = 3(x – 3) Multiply the binomial: 3(x – 3)(x – 3) + 5 3(x 2 – 6x + 9) + 5 Distribute the “a”: 3*x 2 – 3*6x + 3* x 2 – 18x Add “c” y = 3x 2 – 18x + 32

Quiz # 6 You have a pool put in your backyard. If your backyard is square with a side length of 3x + 4 & your pool is square with a side length of 2x, how much yard is still available for kids to play? Find the area of the backyard: (3x+4) 2 (3x+4)(3x+4) 9x x + 16 Find the area of the pool: (2x) 2 2x * 2x 4x 2 Find the difference between the areas: 9x x (4x 2 ) 5x x + 16

Quiz #7 – An object is launched upward at 64 feet per second from a platform 80’ high. What will be the object’s maximum height? Use the quadratic formula: h = -16tx + 64t + 80 Use the graphing calculator Graph the quadratic function Analyze the graph What is the maximum?

Solutions – Quiz #1 & 5 Find the solutions for 4x 2 + 6x = 20 Collect all terms on the same side of the equals 4x 2 + 6x – 20 = 0 Graph quadratic Analyze graph Record “zeros” Find the zeros for x 2 – 18x = 19 Collect all terms on the same side of the equals x 2 – 18x – 19 = 0 Find factors of -19 that add to -18 (x+1)(x-19) Set each factor equal to 0 & solve x+1=0x-19= x=-1 x=19

Transformations in Vertex Form Converted to Standard Form Use Quiz #12 Original Equation: y = (x - 0) Translated left 2 and down 4 New Equation: y = (x - -2) – 4 y = (x + 2) 2 – 3 Standard Equation: y = (x + 2)(x + 2) – 3 y = x 2 + 4x y = x 2 + 4x + 1

Quiz #10 – Read the Graph What are the increments of “x”? What are the increments of “y”? What is the label for “x”? What is the label for “y”? Maximum height? Time to reach max height? Time in the air? Starting point?

Factoring - Quiz #3 Factor x 2 – 81 = 0 Notice that both are perfect squares Notice there is no “b” term Notice that “c” is subtracted or negative What does the sign of “c” tell you? Start the factoring with (x + )(x - ) Then take the square root of 81 (x + 9)(x – 9)

Quadratic Regression – Quiz #13 Open a document using a list or spreadsheet Label the 1 st column “x” and the 2 nd column “y” Enter the x and y values Click menu, statistics, stat calculations, quadratic regression Notice the boxes labeled a, b & c To the right are the value to replace a, b & c in the standard form of the quadratic equation

Domain & Range – Quiz #12 What is the domain if it isn’t limited? What do you use of the vertex to work with range? How do you know if it’s ≤ or ≥?

Identify Factors from Graph – Quiz #9 What are the zeros on the graph? (-4.75, 0) and (.5,0) Pick one – I picked the second one: x = ½ To be a factor it must equal 0 So... Get rid of the denominator first by multiplying everything by 2 2x = 1 Still not equal to 0 so... Subtract 1 from both sides 2x = x-1 = 0