Transformations
Describe the transformation for:
g(x) = (x + 3)2 -2
What is a translation of 3 units left and 2 units down?
Properties of: f(x) = x2 + x - 2
What is opens up, axis = -1/2, vertex = (-1/2, -9/4), y-int = -2, and min= -9/4?
Find the zeros of each function by factoring:
f(x) = x2 - 5x - 6
What is (x - 6)(x + 1); 6 and -1?
Solve the equation:
x2 + 12x + 36 = 28
What is -6 +- 2square root 7
Solve each equation:
1/3x2 = -27
What is +-3i?
f(x) = -x2 + 6x - 8
What is a reflection, translation 3 units right, and 1 unit up?
Properties of: f(x) = 3x2 + 2x - 8
What is opens up, axis = -1/3, vertex = (-1/3, -25/3), y-int = -8, and min= -25/3?
Find the zeros of each function by graphing:
f(x) = -x2 - 2x + 3
What is -3 and 1?
Complete the square and write it as a binomial
x2 - 14x + _____
What is x2 - 14x + 49... (x - 7)2?
Solve each equation:
x2 + 10x + 29 = 0
What is -5 +- 2i?
g(x) = 4/3 (x + 2)2 - 5
What is a vertical stretch by 4/3, translation left 2 units, and down 5 units?
Properties of: h(x) = .5x2 - 2x - 4
What is opens up, axis = 2, vertex = (2, -6), y-int = -4, and min= -6?
Find the zeros of each function by factoring:
f(x) = x2 - 8x
What is x(x - 8); 0 and 8?
Solve each equation by completing:
3x2 - 24x = 27
What is -1 and 9?
Find the zeros of the function:
h(x) = x2 - 16x + 68
What is 8 +- 2i?
The parent function f(x) = x2 is vertically compressed by a factor of 1/3 and translated 2 units right and 4 units down to create g.
What is g(x) = 1/3(x-2)2 -4?
Properties of: f(x) = -1/2(x + 5)2 - 8
What is opens down, axis = -5, vertex = (-5, -8), y-int = -20.5, and max = -8?
Write a quadratic function in standard form for each set of zeros: 6 and 2.
What is (x - 6)(x - 2) ... x2 - 8x + 12?
Solve each equation by completing:
x2 = 12x - 20
What is 2 and 10?
Name the conjugate: -3 + 3i
What is -3 - 3i?
The parent function f(x) = x2 is reflected across the x-axis and translated 5 units left and 1 unit up to create g.
What is g(x) = - (x + 5)2 + 1?
Properties of: f(x) = -(x - 3)2 + 1
What is opens down, axis = 3, vertex = (3, 1), y-int = -8, and max = 1?
Find the zeros of each function by graphing:
f(x) = -2x2 + 4x
What is 0 and 2?
Write each function in vertex form, and identify its vertex:
f(x) = 5x2 - 50x + 128
What is g(x) =5(x - 5)2 + 3 and (5, 3)?
Find the values of x and y:
5(x - 1) + (3y)i = -15i - 20
What is
5(x - 1) = -20 (3y)i = -15i
x - 1 = -4 divide by 3i
x = -3 y = -5 ?