Hon Math III: Unit 3
QUADRATICS: VERTEX FORM INTRODUCTION
1) Identify the VERTEX of the parabola.
2) Draw the AXIS of SYMMETRY for the parabola and provide its equation.
3) Does the graph have Min or Max for its DOMAIN or RANGE?
Graph #1:
Graph #2:
Graph #3:
(-3, 18)
(2, 25)
(1, 0)
(-5, 0)
(0, 21)
(-3, 0)
(7, 0)
(0, -5)
(-6, 0)
(0, 0)
(-2, -9)
Graph #4:
Graph #5:
Graph #6:
(8, 0)
(0, 2)
(4, -3)
(-4, 0)
(-1, -3)
(0, -2)
(0, -11)
(0, -2)
(0, -4)
Graph #7:
(0, 3)
Graph #8:
Graph #9:
(0, 12)
(-4, 1)
(0, 3)
(6, 0)
(2, 0)
(9, 0)
(0, -1)
(4, -4)
Review of Transformations
Parent Function: f(x)
Transformed Function: af(x – h) + k
Original Vertex: (0, 0)
New Vertex: (h, k)
“a” – value: Vertical Stretch: |a|> 1
Vertical Shrink: 1 > |a|> 0
Vertical Flip/Reflect: a < 0
“h” – value: Horizontal Shift  LEFT: h < 0 (Add statement)
RIGHT: h > 0 (Subtract statement)
“k” – value: Vertical Shift  DOWN: k < 0 (subtract statement)
UP: k > 0 (Add statement)
Parent Function: f(x) = x
2
Find the equation of the parabola graphs
Transformed Function: a(x – h)2 + k
1) Use the new vertex to identify the horizontal and vertical shift values (h,k)
2) Use another point on the graph (x, y) and the vertex values (h, k) to solve for a-value
Graph #1: y = a(x – h)2 + k
Graph #2: y = a(x – h)2 + k
Graph #5: y = a(x – h)2 + k
Graph #3: y = a(x – h)2 + k
Graph #6: y = a(x – h)2 + k
Find the equation of the “Sideways Quadratic Graph”: Graphs #4, 6, 7, and 9
Resembles TWO Square Root Graphs
Parent Function:
f ( x) 
x
Transformed Function:
f ( x)  a x  h  k
1) Use the new vertex to identify the horizontal and vertical shift values (h,k)
2) Use another point on the graph (x, y) and the vertex values (h, k) to solve for a-value
3) Solve the transformed equation
y  a x  h  k for x.
Graph #4:
y a xhk
Graph #6:
y a xhk
Graph #7:
y a xhk
Graph #9:
y a xhk
SUMMARY OF QUADRATIC GRAPHS (PARABOLAS)
Vertical Parabolas
Horizonal Parabolas
(Type 1: Up and Down)
(Type 2: Right and Left)
Vertex Form:
y  a( x  h)2  k
Vertex Form:
x  a( y  k ) 2  h
Vertex: (h, k)
Vertex: (h, k)
Axis: x = h (vertical line)
Axis: y = k (horizontal line)
Opens: a > 0 UP; a < 0 DOWN
Opens: a > 0 RIGHT; a < 0 LEFT
QUADRATICS: VERTEX FORM CLASS/HOMEWORK
For #1 – 9: In each vertex form equation, Identify …
a)VERTEX: (h, k)
b) AXIS OF SYMMETRY: y = … or x = …
c) OPENING DIRECTION: Up, Down, Left, Right
1) y = -6(x + 2)2 – 1
2) y = (x – 4)2 – 7
3) x = (y – 3)2 + 5
VERTEX:
VERTEX:
VERTEX:
AXIS:
AXIS:
OPEN:
OPEN:
4) x = -3(y + 2)2 + 1
5) y =2(x )2 + 9
6) x = (y – 5)2
VERTEX:
VERTEX:
VERTEX:
AXIS:
AXIS:
AXIS:
OPEN:
OPEN:
OPEN:
AXIS:
DIRECTION:
7) y = 7(x + 9)2 + 8
8) x = 2(y + 4)2 – 2
9) y = -3(x – 2)2 – 5
VERTEX:
VERTEX:
VERTEX:
AXIS:
AXIS:
AXIS:
OPEN:
OPEN:
OPEN:
For #10 – 17: Find the VERTEX FORM equation for a parabola given the
VERTEX, ANOTHER POINT, and the OPENING DIRECTION of the graph.
10) Vertex: (1, 3)
Point: (-2, -15)
Open: VERTICAL
13) Vertex: (4, 3)
Point: (22, 0)
Open: HORIZONTAL
16) Vertex: (-4, -1)
Point: (0, -33)
Open: VERTICAL
11) Vertex: (-3, 0)
Point: (3, 18)
Open: VERTICAL
14) Vertex: (-5, -2)
Point: (-2, 1)
Open: HORIZONTAL
12) Vertex: (10, -4)
Point: (5, 6)
Open: VERTICAL
15) Vertex: (-3, 5)
Point: (1, 3)
Open: HORIZONTAL
17) Vertex: (1, -2 )
Point: (-11, -4)
Open: HORIZONTA