1. Algebra 2: Unit 3 - Vertex Form
UNIT 1 REVIEW of TRANSFORMATIONS of a GRAPH
f(x)
Original (Parent) Graph
a•f(x – h) + k
Transformed Graph
“a” – value
Stretch or Shrink Graph and Flips for negative
“h” – value
Shifts the Graph Right or Left
“k” – value
Shifts the Graph Up or Down
For quadratic graphs #1 - 6:
y = a(x – h)2 + k
TRANSFORMED QUADRATIC FUNCTION
y = x2
QUADRATIC FUNCTION
(ORIGINAL)

2. FIND THE EQUATION of the Quadratics in Graphs #1 - 6
Step #1: Use the vertex to indicate the horizontal (h) and vertical (k) changes
Step #2: Use another point on the graph to help determine the “a”- value (Hint: The direction it opens indicates the sign)
Graph #1:
y = a(x – h)2 + k
Graph #2:
y = a(x – h)2 + k

3. Graph #3:
y = a(x – h)2 + k
Graph #4:
y = a(x – h)2 + k

4. Graph #5:
y = a(x – h)2 + k
Graph #6:
y = a(x – h)2 + k

5. a (+ up; – down) a (+ right; –left) Vertex Form Vertex Form Vertex:
QUADRATIC FUNCTIONS – VERTEX FORM SUMMARY
Vertical Parabolas
(Type 1: Up and Down)
Horizontal Parabolas
(Type 2: Right and Left)
Vertex Form
Vertex Form
Vertex:
Vertex:
(h, k)
(h, k)
Axis:
x = h
Axis:
y = k
Rate:
a (+ up; – down)
Rate:
a (+ right; –left)

6. Find VERTEX FORM EQUATION:
Given Vertex & Point
Plug vertex (h, k) into appropriate vertex form equation and use another point (x, y) to solve for “a”.
[A]
Opening Vertical
Vertex: (2, 4)
Point: (-6, 8)
[B]
Opening: Horizontal
Vertex: (- 4, 6)
Point: (2, 8)

7. Vertex Form to Standard Form of Quadratic Functions
FOIL the squared statement.
Distribute a-value
Combine Like Terms
[B]
[A]

8. [D]
[C]

9. Algebra 2: Unit 3 - Vertex Form
Standard Form to Vertex Form of Quadratic Functions
Vertical Parabolas ( y = )
Graph the Equation in [Y =]
Find Vertex using MIN or MAX command in [CALC]
a – value is the same in standard and vertex form.
[B]
[A]
a - value:
a - value:
Vertex:
Vertex:
Equation:
Equation:

10. Horizontal Parabolas ( x = )
Vertical Parabolas ( y = ): Continued
[D]
[C]
a - value:
a - value:
Vertex:
Vertex:
Equation:
Equation:
Horizontal Parabolas ( x = )
Switch the variables and Graph the Equation in [Y =]
Opens Up = Opens Right
Opens Down = Opens Left
Find Vertex using MIN or MAX command in [CALC]
Switch the Min or Max Ordered Pair for actual vertex
a – value is the same in standard and vertex form.

11. Horizontal Parabolas Practice
a - value:
a - value:
Sketch:
Sketch:
Vertex:
Vertex:
Equation:
Equation:

12. a - value: a - value: Sketch: Sketch: Vertex: Vertex: Equation:
[D]
[C]
a - value:
a - value:
Sketch:
Sketch:
Vertex:
Vertex:
Equation:
Equation: