Download Parts of quadratics parabolas

Parts of quadratics and parabolas in standard form
2
Standard form = 𝑎𝑥 + 𝑏𝑥 + 𝑐
Standard Form
𝑎𝑥 + 𝑏𝑥 + 𝑐
2𝑥 + 8𝑥 − 5
How to write
answer
To find x:
To find x:
(x,y)
2
Vertex
−𝑏
2𝑎
To find y:
Plug answer for x into x
and solve for y
Example
2
−8
2(2)
=
−
8
4
=
−2
To find y:4
Plug answer for x into x
and solve for y
2
2(− 2) + 8(− 2) − 5
2(4) − 16 − 5
8 − 16 − 5
− 13
Vertex = (-2,-13)
Direction of
opening
If a>0 then it opens up
If a<0 then it opens down
a=2
2>0 so it opens up
Opens up/down
Maximum
or
minimum
If it opens up, there is a
minimum
If it opens down there is a
maximum
Opens up so there is a
minimum
y=#
min/max is the y from the
vertex
Minimum: y=-13
X from the vertex
Vertex = (-2,-13)
Axis of
Symmetry
Vertex = (-2,-13)
Or may just want
the number
without y=
x=#
Axis of Symmetry: x=-2
Domain
Domain for
quadratics/parabolas is
always:
All real numbers
(− ∞, ∞)
Domain for
quadratics/parabolas is
always:
All real numbers
(− ∞, ∞)
(− ∞, ∞)
Range
Range is the lowest to
highest point
*y is the y from the vertex*
Vertex = (-2,-13)
(#,∞)
OR
(-∞,#)
If opens up:
(𝑦, ∞)
Range: (− 13, ∞)
If opens down:
(− ∞, 𝑦)
Opens up