Vertex: The maximum or minimum value (y-coordinate) of a parabola. Its coordinates are written (h, k). The max or min value is always k.

Axis of Symmetry: The line (of reflection) through which one half of the parabola “folds” onto the other half. For a vertical parabola its equation is always [x=h]

Roots aka X-Inercepts aka Zeros: The x-coordinate of the point where the parabola crosses the x-axis. A parabola can have 0,1 or 2 roots.

The Standard form for the equation of a Parabola: F(x) =

**a**(x-h)2 +

**k**1

The Role of Parameter a:

A > 0 the parabola opens up

A< 0 the parabola opens down

1a1 > 1 the arms of the parabola are “skinner” than f(x)=x2

0 < 1a1 < 1 the arms of the parabola are “wider” than f(x)=x2

“If the vertex is above the x-axis it has no roots when the parabola is opening up.”

“If the vertex is below the x-axis it has no roots when the parabola is opening down.”

The Role of Parameter h:

H > 0 the parabola shifts right h units

H < 0 the parabola shifts left h units

[ Warning: WATCH THE SIGN OF H ]

Example: f(x) = (x+2)2

H = -2 (in an equation if the sign is positive h its negative

If the sign is negative h its positive)

The Role of Parameter k:

K > 0 the parabola shifts up k units

K < 0 the parabola shifts down k units

H tells you the x-coordinate of the vertex

K tells you the y-coordinate of the vertex

if Y = (x-3)2 +2, the parabola will be open up

if Y =

**5**(x-3)2 + 2, the parabola becomes "skinnier" but still opens up

if Y =

**-5**(x-3)2+2, the parabola is skinny but opens down because when

**a**is negative, the parabola always opens down

Homework for today: excersise 4

TO CONCLUDE MY SCRIBE POST THE NEXT SCRIBE IS GOING TO BE... DUN DUN DUN... JOSEPH ! GOOD LUCK JOSEPH, I KNOW YOU'LL DO WELL! :)

Hey, good job crysta =). Does anyone care to explain this..

ReplyDelete[ Warning: WATCH THE SIGN OF H ]

Example: f(x) = (x+2)2

H = -2 (in an equation if the sign is positive h its negative

If the sign is negative h its positive)

I was looking it over and I don't understand why they'd be their opposite signs.

Good clear scribe. You had excellent use of colour and your explanations were easy to understand.

ReplyDeleteKeep it up. Who can answer eedce question in her comment??

Mr. Harbeck

Sargent Park School

Hi eedce,

ReplyDeleteremeber the standard formula...f(x)=a(x-h)^2 +k. Look carefully at the sign before "h"..its "-" right?.

that means whatever h was...it's been forced to come along with the negetive sign in the formula. example...if h=-3 in the graph ....we have to put that in the equation...so the equation will be

f(x)=a(x-(-3))^2 + k

=a (x+3)^2 +k

here h looks like its +3...but originally h was -3....

in the other side..

if h= 3

equation will be

f(x)= a(x-(+3))^2 + k

=a(x-3)^2 + k

here...h looks like its -, but originally h was +3.

so, what you have to look for is: WHAT KIND OF SIGN (+/-) INTERACTED WITH THE - SIGN IN THE EQUATION TO GIVE US THE SIGN OF h THAT WE SEE IN THE EQUATION.

I hope that was helpfull

Natnael

Wowzorcake. Thank you natnael for taht wonderfull explination. Oh yea! good job Crysta on your scribe post it was awsome.

ReplyDeleteCongatulations Nathanial on leaving such an informative comment. thanks for helping eedce

ReplyDeleteMr. Harbeck

Sargent Park School

Thanks for clearing that up for me Natnael! =) It makes much more sense now, thanks again.

ReplyDeleteYou'r welcome

ReplyDelete