Algebra IIB Mrs. Crespo GRAPHING THE QUADRATIC y – k = a(x – h) 2

THE BASIC GRAPH OF A QUADRATIC FUNCTION (0,0)

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) 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) = a (2 + 1) 2 -3 = a (3) 2 -3 = 9a

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 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 odd (just draw a reasonable graph without finding the intercepts at this time) page all Algebra

ACKNOWLEDGEMENT McDougall Little Algebra and Trigonometry Book 2 by Brown, Dolciani, Sorgenfrey, Kane 2011 PowerPoint by Mrs. Crespo for Algebra IIB