Stephanie's Reflection

Graphing Parabolas
~Descriminate tells you how many intercepts a graph has
b^2-4ac
if +ve 2 x-intercepts
if -ve no x-intercepts
if 0 1 x-intercept
~Axis of Symmetry x=-b/2a if non-standard form
~Vertex (-b/2a, f(-b/2a)) for non-standard form
~to find the intersections
solve for y
set equal
solve for x
plug back in

EG: graph y-2x^2-8x+5
1)open up or down? +2x=up
2)how many intercepts? b^2-4ac = -8^2-4x2x5=24
2 x-intercepts
3)x-intercepts? 2x^2-8x=-5
x^2-4x+4=-5/2+4
sqrt(x-2)^2=sqrt3/2
x-2=sqrt3/sqrt2 sqrt2/sqrt2=sqrt6/2
(sqrt6/2 +2, 0) (-sqrt6/2 +2, 0)
4)y-intercepts? 2(0)^2-8(0)+5
(0,5)
5)axis of symmetry? x=-b/2a = 8/2x2 = 8/4 = 2
x=2
6)vertex? (2,-3)
2x2^2-8x2+5=-3

EG: y=x^2-6x
1)up
2)b^2-4ac 6^2-4x1x0 = 2x-intercepts
3) y=x(x-6)9
x=0 x=6
(0,0) (6,0)
4)0^2-6x0=0
(0,0)
5)x=-b/2a = 6/2x1=3 x=3
6)3^2-6x3=-9
(3,-9)

EG: y=4-2x
y=x^2-6x+8
4-2x=x^”2-6x+8
0=x^2-4x+4
x^2-4x+4=0
(x-2)(x-2)=0
x=2
4-2x2=0
(2,0)

EG: y=4x^2-8x+2
-8^2-4x4x2=
64-32=32
=2x-intercepts
2x^2-8x=-2
x^2-2x+1=-1/4+1
sqrt(x-1)^2=sqrt(3/4)
x-1=sqrt(3/4)
x=sqrt(3/4)+1
(sqrt(3/4)+1,0) (-sqrt(3/4)+1,0)
(0,2)
8/2x4=1
x=1
(1,-2)
4x1^2-8x1+2=-2

EG: y=1/2x^2+4x+8
4^2-4x1/2+8=16-16=0 no x-intercepts
(0,8)

EG:5x^2+5x+1=0
-b+/-sqrt(b^2-4ac)/2a
a=5
b=5
c=1
-5+/-sqrt(5^2-4x5x1)/2x5
-5+/-sqrt5/10
(-5-sqrt5/10,0) (-5+sqrt5/10,0)

EG: x^2-2x-2=0
x?^2-2x+1=2+1
x^2-2x+1=3
sqrt(x-1)^2=sqrt3
x-1=+/-sqrt3
x=+/-sqrt3+1
(1+sqrt3,0) (1-sqrt3,0)

COMPLETE THE SQUARE
x^2+3x-1=0
x^2+3x+9/4=1+9/4
sqrt(x+3/2)^2=sqrt13/4
x+3/2=+/-sqrt13/2
x=-3/2+/-sqrt13/2
etc.