Equations / Misc
f(x)=x^2
y=x^2−4
Shift down 4
y=(x−3)^2+2
(3,2)
y=x^2+6x+5
(-3,-4)
y=4(x+2)^2−8
Stretch 4, Left 2, Down 8
What is the axis of symmetry in VERTEX form?
x=h
y=x^2+6x+8
Axis of symmetry at (-3,-1)
y=−2(x+4)^2−1
(-4,-1)
y=−x^2+4x+1
(2,5)
y=−2(x−5)^2+7
Reflect across the x-axis
Stretch 2
Right 5
Up 7
What is the axis of symmetry in standard form?
x=-b/2a
y=(x−2)^2+3
Shift right 2, up 3
Vertex: (2,3)
y=1/2(x−5)^2−6
(5,-6)
y=2x^2−8x+7
(2,-1)
y=−5/2(x−3)^2−2
Reflect across x-axis
Stretch by 5/2
right 3
down 2
Explain how you know if the vertex will be a minimum or maximum?
If there's a negative in front of the x^2 the parabola will open downwards and have a maximum.
If there's a positive in front of the x^2 the parabola will open upwards and have a minimum.
y=−2x^2−4x−1
Axis of symmetry (-1,1)
Opens downward
y=−3(x+1)^2+4
(-1,4)
y=−3x^2−6x+9
(-1,12)
y=3/4(x+1)^2+5
Compress 3/4
Left 1
Up 5
Why do absolute value graphs and quadratic graphs look similar?
A negative number squared is a positive. A negative in absolute value bars is also a positive. Creating the "U" and "V" shape.
y=−1/2(x−2)^2+1
Vertex: (2,1)
Opens Downwards, Compress 1/2, right 2, up 1
y=4(x−2)^2−8
(2,-8)
y=1/2x^2−4x+2
(4,-6)
y=−1/3(x−6)^2+4
Reflect across x-axis
Compress 1/3
Right 6
Up 4