Verbal Transformations
Zack sketches a parabola with a vertex at the origin that opens downward. It contains the points (1,-1), (-1,-1), (2,-4), (-2,-4). What is the equation of Zack's function?
y = -x2
Evaluate the Function at f(-1):
f(x)= x2 + 6
f(x)= x2 + 6
f(x)= (-1)2 + 6
f(x)= 1 + 6
f(x)= 7
y = x2
(0,0)
Flipping your function across either the x or y axis
What is Reflection
y = (x+1)2
Translated 1 unit left
Dakota translates the quadratic parent function 10 units to the right. What is the equation of Dakota's function?
y = (x-10)2
Evaluate the Function at f(3):
f(x)= 2x2
f(x)= 2x2
f(x)= 2(3)2
f(x)= 2(9)
f(x)= 18
y = (x-10)2
(10,0)
f(x)=a(ax-h)2+k is known as the _____ form equation
What is Vertex form?
y = (1/3)x2
Vertically compressed
Gloria transforms the quadratic parent function by translating the parabola 8 units up and 6 units right. What is the equation of Gloria's parabola?
y = (x-6)2 + 8
Evaluate the Function at f(-2)
f(x)= -0.5(x+6)2
f(x)= -0.5(x+6)2
f(x)= -0.5((-2)+6)2
f(x)= -0.5(4)2
f(x)= -0.5(16)
f(x)= -8
y = (x+1)2 + 9
(-1,9)
A numerical relationship where every input (X-value) has EXACTLY one output (y-value)
What is a Function?
y = -(x+2)2
Reflected across the x-axis, and translated 2 units to the left
Mike begins with the quadratic parent function. Mike transforms a quadratic function by stretching it vertically by a factor of 4. What is the equation of the transformed function? What is Mike's equation?
y = 4x2
Evaluate the Function at f(1)
f(x)= 0.25(x+1)2 -3
f(x)= 0.25(x+1)2 -3
f(x)= 0.25(1+1)2 -3
f(x)= 0.25(2)2 -3
f(x)= 0.25(4) -3
f(x)= 1 -3
f(x)= -2
y = 5x2
(0,0)
Describe the vertical line test. Draw 2 examples of it on the board
Vertical Line test is used to determine whether or not a graph is an actual function. If your vertical line touches your graph only once it is a f(x) if it touches it more than once it is NOT a f(x).
y = (x-3)2 + 1
Translated 3 units to the right and 1 unit up.
Ashanti transforms a quadratic function by compressing it vertically by a factor of .5 and translating the parabola 2 units down and 1 unit to the left. What is the equation of the transformed function?
y = .5(x+1)2 - 2
Evaluate the Function at f(2)
f(x)= 1.5(x-4)2 +1
f(x)= 1.5(2-4)2 +1
f(x)= 1.5(-2)2 +1
f(x)= 1.5(4) +1
f(x)= 6 +1
f(x)= 7
y = 2(x+6)2 +3
(-6,3)
Define domain and range.
When writing the terms for domain and range we always use always this form. It is known as ____
Domain - complete set of x values that makes your function work
Range - all the real y values from your x-values
Interval notation: [0,∞) or (-∞,∞)
y = -2(x-4)2 + 15
Vertically stretched, reflected across the x-axis, and translated 4 units to the right and 15 units up.