Graph/Describe transformations
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=(x-5)2
The function f(x) had a horizontal translation 5 units right.
What is the formula for quadratics in vertex form?
f(x)=a(x-h)2+k
What is the equation for quadratics in standard form?
f(x)=ax2+bx+c
A u-shaped graph created with a quadratic equation is called what?
What is a parabola
What is the formula to find the axis of symmetry?
x=-b/2a
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=(x+3)2-1
The function f(x) had horizontal translation of 3 units left and a vertical translation of 1 unit down.
What is the vertex and axis of symmetry? Graph the function.
f(x)=(x-3)2+4
Vertex(3,4)
Axis of symmetry: x=3
What is the formula to find the axis of symmetry when in standard form?
x= (-b)/2a
The highest or lowest point of the parabola is called..
Vertex
When given a>1 the graph (parabola) will ________ vertically
What is stretch or get closer to the y axis?
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=3(x-4)2
The function f(x) had a horizontal translation 4 units right and a vertical stretch of 3.
What is the vertex and axis of symmetry? Graph the function.
f(x)=(x+4)2-2
Vertex: (-4,-2)
Axis of symmetry: x=-4
What is the vertex, axis of symmetry, and the y-intercept?
f(x)= x2-8x+12
x = 8/2(1) = 4, Axis of Symmetry: x = 4
(4)^2 -8(4) + 12 = 16 - 32 + 12 = -4
vertex (4,-4)
After Graphing: y-intercept:(0,12)
What is A in this equation? x^2+15x-7
What is 1?
Find the axis of symmetry for the following quadratic.
y= x^2+8x-5
What is x =-4
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=1/2x2+7
The function f(x) compressed/widened by a factor of 1/2 and a vertical translation of 7 units up.
What is the vertex and axis of symmetry? Graph the function.
f(x)= -2(x+1)2
Vertex: (-1,0)
Axis of Symmetry: x=-1
What is the vertex, axis of symmetry, and the y-intercept?
f(x)= -x2-8x-15
X = 8/2(-1) = -4, Axis of symmetry: x=-4
f(x) = -(-4)^2 -8(-4) -15 = -16 +32 -15 = 1
Vertex: (-4,1)
Graphing shows: y intercept: (0,-15)
What is a factor of two (or more) other numbers called (Specifically, the highest factor)?
What is the GCF?
When given y =a(x+h)^2 in the vertex formula,
y = a(x - h)^2, the graph will shift ______ horizontally
What is left?
Graph the parent function, then graph f(x). Describe the transformation.
f(x)=-4(x-6)2-2
The function f(x) is reflected over the x - axis and has a vertical stretch of 4. The function has a horizontal translation of 6 units right and a vertical translation of of 2 units down
What is the vertex and axis of symmetry? Graph the function.
f(x)=1/3x2+2
Vertex: (0,2)
Axis of symmetry: x=0
What is the vertex, axis of symmetry, and the y-intercept?
f(x)= 2x2+4x-6
x = -4/2(2) = -1, Axis of Symmetry: x=-1
f(x)= 2(-1)2+4(-1) -6 =2 - 4 - 6 =-8
Vertex: (-1,-8)
y intercept: (0,-6)
Find the x-intercepts, vertex, and axis of symmetry. Graph the function. (Lesson 8.4)
f(x)=-1/2(x+2)(x-4)
Vertex: (1, 4.5)
Axis of symmetry: x=1
X intercept: (-2,0) & (4,0)
If y = 1/3(x-2)2 - 1, Identify the transformations for the following:
a (1/3) ->
h (-2) ->
k (-1) ->
What is
3 -> Widens (compresses by factor of 1/3)
-2 -> Move to the right 2
-1 -> Move down 1