SCRIBE FOR THE DAY!!!!

Today in class we did work in our math dictionary about parabolas. Heres some of the things we reviewed:

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 + k1

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! :)