Quadratics
description
Transcript of Quadratics
Quadratics
y = x 2
Flips up because positive
value
Doesn’t move left or right on x axis. Stays at 0
Doesn’t move up or
down y axis. Stays
at 0
This is the “parent”.
y = 1/2 x2
Flips up because negative
value
Doesn’t move left or right.
Stays at 0
Doesn’t move up or
down. Stays at 0
Makes parabola
wider
y = -4x2 + 2
Flips down because negative
value
Doesn’t move left or right.
Stays at 0
Moves up 2 on y axis
Makes parabola skinnier
y = 1/2 (x+3)2
Flips up because negative
value
Moves left 3 on x axis Doesn’t
move up or down.
Stays at 0
Makes parabola
wider
y = (x – 4)2 + 5
Flips up because positive
value
Moves right 4 on x
axis
Moves up 5 on y axis
y = -(x + 2)2 - 5
Flips down because negative
value
Moves left 2 on x axis
Moves down 5 on
y axis
y = - 3(x – 4)2 + 9
y = x2 – 7x + 12
y = (x – 3)(x + 6)
Quadratic Family
Moves parent right 4 and up 5.
This is the NEW vertex.
x intercept:
y intercept:
vertex:
D:
R:
none
(0,21)
(4,5)
{ y : y > 5}
y = x2 – 7x + 12
HOW DO YOU FIND THE X
INTERCEPTS?Set y = 0 0 = - 3(x – 4)2 + 9
Minus 9 from both sides.-9 = - 3(x – 4)2 Divide by -3 3 = (x – 4)2
Square Root both sides 1.73 = x – 4
-1.73 = x - 4Solve.(5.73, 0) and (2.27, 0)
HOW DO YOU FIND THE X
INTERCEPTS?Set y = 0 Factor
OR
Quadratic Formula
HOW DO YOU FIND THE VERTEX?
-b2a
This gives you the X
COORDINATE of the vertex. To
find the y, substitute this x into the original and evaluate.
OR You Could
Use the Midpoint of the x
intercepts.
HOW DO YOU FIND THE VERTEX?
Find the midpoint of the x intercepts. Then substitute that x into the original to find it’s
y coordinate.
y = (x + 8)(x - 2)
HOW DO YOU FIND THE X
INTERCEPTS?Set each factor equal to 0 and solve. (Take the opposite of them.)
(-8,0) and (2,0)
6th hour ends. They need rest of this and FF1
y = (3x + 2)(5x - 2)
Quadratic Family
x intercept:
y intercept:
vertex:
D:
R:
(-2/3, 0) (2/5, 0)
(0,-4)
(-2/15, -4.27)
{ y : y > -4.27}
y = x2 – 7x + 12
Quadratic Family
x intercept:
y intercept:
vertex:
D:
R:
(4, 0) (3, 0)
(0,12)
(3.5, -.25 )
{ y : y > -.25}
y = x2 + 6x + 1
Quadratic Family
x intercept:
y intercept:
vertex:
D:
R:
NONE
(0,1)
{ y : y > -8}
Because there are NO x intercepts
YOU MUST USE –b/2a to find the
VERTEX!!!(-3, -8)
x2 – 9
4x2 – 49
Factor(2x – 7)(2x + 7)
16x2 – 46x + 49
Factor(4x – 7)(4x - 7)
x2 – 7x - 18
Factor(x + 9)(x - 2)
12x4 – 3x3
Factor(3x3)(4x + 1)
(x + 10)(x - 2)
QUICK FOILx2 + 8x - 20
(x - 3)(x - 2)
QUICK FOILx2 - 5x + 6
(x – 5)2
QUICK FOILx2 - 12x + 36
(3x + 2)2
QUICK FOIL9x2 + 12x + 4