Algebra IIB

Mrs. Crespo 2012-2013

GRAPHING THE QUADRATIC y – k = a(x – h)2

THE BASIC GRAPH OF A QUADRATIC FUNCTION

(0,0)

PARABOLA

THE “a” in y – k = a(x – h)2 .

(0,0)

• IF a > 0, the parabola opens upward.

• IF a < 0, the parabola opens downward.

THE “k” in y – k = a(x – h)2 .

• IF k > 0, the parabola moves up “k” units.

• IF k < 0, the parabola moves down “k” units.

(0,0)

THE “h” in y – k = a(x – h)2 .

• IF h > 0, the parabola moves right “h” units.

• IF h < 0, the parabola moves left “h” units.

(0,0)

ALL TOGETHER AND MORE: y – k = a(x – h)2

To plot for now, we need:

• vertex (h, k)

• axis of symmetry x = h

• IF a > 0, the parabola opens upward.

• IF a < 0, the parabola opens downward.

• IF k > 0, the parabola moves up “k” units.

• IF k < 0, the parabola moves down “k” units.

• IF h > 0, the parabola moves right “h” units.

• IF h < 0, the parabola moves left “h” units.

V (h,k)

V (h,k)

x = h

x = h

GRAPH y + 2 = (x + 3)2

• a = 1 > 0, the parabola opens upward.

• k = -2 < 0, the parabola moves down 2 units.

• h = -3 < 0, the parabola moves left 3 units.

• vertex (h, k) = (-3, -2)

• axis of symmetry x = h is

x = -3.

V (-3,-2)

x = -3

GRAPH y - 3 = -(x + 1)2

• a = -1 < 0, the parabola opens downward.

• k = 3 > 0, the parabola moves up 3 units.

• h = -1 < 0, the parabola moves left 1 unit.

• vertex (h, k) = (-1, 3)

• axis of symmetry x = h is

x = -1.

FIND AN EQUATION OF THE PARABOLA

• A parabola has vertex (-1, -2) and contains the point (2, -5).SOLUTION:

Plug in vertex (h, k) on y – k = a(x – h)2 So, y – (-2) = a(x – (-1))2 Then, y +2 = a(x + 1)2

Solve for a with point (2, -5) -5 +2 = a(2 + 1)2

-3 = a(3)2 -3 = 9a

= a

= a

The equation of the parabola is:

y +2 = (x + 1)2

FIND AN EQUATION OF THE PARABOLA

• A parabola has vertex (2, -3) and y-intercept 9.SOLUTION:

Plug in vertex (h, k) on y – k = a(x – h)2 So, y – (-3) = a(x – 2)2 Then, y +3 = a(x -2)2

Solve for a with point (0, 9) 9 +3 = a(0 - 2)2

12 = a(-2)2 12 = 4a

= a

3 = a

The equation of the parabola is:

y +3 = 3 (x - 2)2

QUEST 7-5

• Graph y + 2 = (x – 1) 2

• Find an equation of the parabola with vertex (4,5) and contains (5,3)

• Find an equation of the parabola with vertex (-1, -2) with a = -2.

HOMEWORK 7-5

• Page 331

page 331 1-12 odd (just draw a reasonable graph without finding the intercepts at this time)

page 332 19-21 all

Algebra

ACKNOWLEDGEMENTMcDougall Little

Algebra and Trigonometry Book 2

by

Brown, Dolciani, Sorgenfrey, Kane

2011

PowerPoint by Mrs. Crespo

forAlgebra IIB2012-2013