Algebra IIB Mrs. Crespo 2012-2013 GRAPHING THE QUADRATIC y – k = a(x – h) 2.
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Transcript of Algebra IIB Mrs. Crespo 2012-2013 GRAPHING THE QUADRATIC y – k = a(x – h) 2.
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