Vertex Form
Write in vertex form: Quadratic function has a vertical shift down 4, vertical reflection, vertical stretch by a factor of 2, and a horizontal shift left 3
y = -2 ( x + 3 )2 - 4
What is the axis of symmetry for the equation
y = -x2 - 4x ?
x = -2
The range of y = ( x + 1 )2 is..........
y is greater than or equal to 0
Fill in the blank to complete the square:
x2 - 10 x + _____
25
List the transformations for y = -3 ( x +1 )2
1. Shift left 1
2. Vertical stretch by factor of 3
3. Reflect over x-axis (vertical reflection)
Given the following values:
Vertex ( 2,6 ) A ( 0,1 ) B ( x, 1 )
This is the x coordinate of B.
What is 4?
Rewrite f(x) = x2 - 4x +3 in vertex form.
y = ( x - 2 )2 - 1
What is the y intercept for the function
y = 3x2 - x -11?
( 0 -11 )
The range of y = -(x + 3 )2 +3 is...........
y is less than or equal to 3
What is the value of "c" that completes the square for x2 + 14x
c = 49
List the transformations for f(x) = -1/2 ( x - 5 )2 -1
1. Shift down 1.
2. Shift right 5.
3. Vertical compression by factor of 1/2.
4. Vertical Reflection
Given the following values:
Vertex ( -5,2 ) A (-10,8 ) B ( x, 8 )
This is the x coordinate of B.
What is 0?
f(x) = - ( x + 2 )2 - 3 g(x) = - ( x-6 )2 - 1
Which function has the greater maximum value?
g(x) = - ( x-6 )2 - 1
Which of the following is true with respect to the
functions f(x) = x2 -5x +10 and g(x) = -3x2 -3x +10 ?
A They have the same vertex
B They have the same range
C . They have the same y intercept
C . They have the same y intercept
The vertex of a parabola is ( -7, -8 ) and "a" is less than 0. What is the range?
y is less than or equal to -8
Use CTS to convert y = x2 - 12x +15 to
vertex form?
x2 - 12x _______ = -15
X2 - 12x + 36 = -15 + 36
(X - 6)2 - 21 = Y
What is the transformed equation after the parent function has shifted right 6 units, shifted up 3 units and vertically compressed by a factor of 0.25 ?
y = 0.25( x - 6 )2 +3
Given the following values:
Vertex ( 0,6 ) A (-3,10 ) B ( x, 10 )
This is the x coordinate of B.
What is 3?
Rewrite f(x) = 2x2 -16x + 34 in vertex form.
f(x) = 2(x - 4)2 -2
State the max/min for the following function:
f(x) = 2x2 - 4x + 1
Min = -1 when x = 1
Which value, h or k, helps to determine the range?
k
How do you use CTS to convert y = x2 +8X -1 to
vertex form?
X2 + 8X _________ = 1
X2 + 8X + 16 = -1 + 16
(X + 4)2 - 15 = Y
If y = 2(x - 6)2+ 3 is shifted 9 units left and down 4 units, what is the equation of the new function?
y = 2( x + 3 )2 - 1
Given the following values:
Vertex ( 2.5, 6 ) A ( 4,12 ) B ( x, 12 )
This is the x coordinate of B.
What is 1?
Rewrite f(x) = -x2 - 6x -10 in vertex form.
y = - ( x +3 )2 - 1
Find the x-intercepts: f(x) = x2 - 8x + 15
(3, 0) and (5,0)
What is the range of y = x2 - 6x + 2 ?
y is greater than or equal to -7.
How do you write the perfect square for
y = x2 - 18X + 81?
y = ( x - 9)2
What is the equation that results from
y = (x + 9)2 + 3 that has shifted 9 units right
and 3 units down?
y = x2
Given the following values:
Vertex ( -6.5, 0 ) A ( -9, 2 ) B ( x, 2 )
This is the x coordinate of B.
What is -4?