Transforming |x|
What happened to turn f(x)=|x| into:
g(x)=|x|+2
A translation 2 units up.
What happened to turn f(x)=x^2 into:
g(x)=x^2-3
A translation 3 units down
Find the vertex of:
f(x)=x^2
(0,0)
What formula do you use to find the vertex given a quadratic in standard form:
f(x)=Ax^2+Bx+C
First use:
x=(-B)/(2A)
then plug the answer back in to find y.
What does AoS stand for?
Axis of Symmetry
What happened to turn f(x)=|x| into:
g(x)=|x-3|
A translation 3 units to the right.
What happened to turn f(x)=x^2 into:
g(x)=(x+7)^2
A translation 7 units to the left
Find the vertex of:
f(x)=x^2-5
(0,-5)
Find the vertex of:
f(x)=x^2+7
(0,7)
How do you know if a graph has a max or min just from it's equation?
If the "slope" is negative, it has a max.
If the "slope" is positive, it has a min.
What happened to f(x)=|x| to turn it into:
g(x)=|x+2|+4
A translation 2 units to the left and 4 units up.
What happened to turn f(x)=|x| into:
g(x)=(x-5)^2-9
A translation 5 units to the right and 9 units down
Find the vertex of:
f(x)=4(x+3)^2-1
(-3,-1)
Find the vertex of:
f(x)=x^2+4x+3
(-2,-1)
What important point does the Axis of Symmetry pass through?
The vertex
If g(x) is just f(x)=|x| translated 4 units to the right and 1 unit down, then how would you write the equation for g(x)?
g(x)=|x-4|-1
If g(x) is just f(x)=x^2 translated 3 units to the right and 2 unit up, then how would you write the equation for g(x)?
g(x)=(x-3)^2+2
Find 5 points that are on the graph of
f(x)=x^2+3
(0,3), (+-1,4), (+-2,7), (+-3,12), (+-4,19), (+-5,28)... etc.
Find 5 points on the graph of:
f(x)=x^2-2x+1
(-3,16), (-2,9), (-1,4), (0,1), (1,0), (2,1), (3,4), (4,9), (5,16)
Find the AoS and Min/Max value of:
f(x)=-2(x+7)^2-4
AoS: x=-7
Max of -4
If g(x) is just f(x)=|x-2|+1 translated 4 units to the right and 1 unit down, then how would you write the equation for g(x)?
g(x)=|x-6|
If g(x) is just f(x)=(x+3)^2-1 translated 3 units to the right and 4 unit up, then how would you write the equation for g(x)?
g(x)=x^2+3
Find 5 points for the graph of:
f(x)=2(x-3)^2-10
(-1,22), (0,8), (1,-2), (2,-8), (3,-10), (4,-8), (5,-2), (6,8), (7,22)
Find 5 points on the graph of:
f(x)=-2x^2-8x-3
(-6, -27), (-5,-13), (-4,-3), (-3,3), (-2,5), (-1,3), (0,-3), (1,-13), (2,-27)
Find the AoS and Min/Max value of:
f(x)=3x^2-18x+15
AoS: x=3
Min of -12