1. Unit #3: Quadratics 5-3: Translating Parabolas
Essential Question: How is the vertex form used in transforming a quadratic function?

2. 5-3: Translating Parabolas
Yesterday, we explored quadratic equations in polynomial form: y = ax2 + bx + c
Two other forms which are used are x-intercept (factored) form and vertex (transformation) form.
Vertex form of a quadratic function is an equation in the form: y = a(x – h)2 + k
Just like in polynomial form:
If a is positive, the graph opens up
If a is negative, the graph opens down

3. 5-3: Translating Parabolas
y = a(x – h)2 + k
The vertex is found at (h, k)
h: Set what’s inside the parenthesis = 0 and solve for x
k: Take the number that’s being added to the end of the function.
Example
Find the vertex of y = (x + 3)2 – 1
Because a = 1 (nothing in front of the parenthesis):
The graph opens up.
x + 3 = 0 → subtract 3 on each side → x = -3
h = -3, k = -1
The vertex is at (-3, -1).

4. 5-3: Translating Parabolas
Determine the vertex of the quadratic function and whether the graph opens up or down.
y = -3(x + 2)2 + 4
Opens:
Vertex:
y = 2(x – 2.5)2 – 5.5
y = -½(x – 2)2
Down
(-2, 4) Up
(2.5, -5.5)
Down
(2, 0)

5. 5-3: Translating Parabolas
To find the y-intercept:
Simply substitute “0” in for x and simplify
Example: y = -2(x – 3)2 + 4
y = -2(0 – 3)2 + 4
= -2(-3) 2 + 4
= -2(9) + 4 =
= -14
The y-intercept is at (0, -14)

6. 5-3: Translating Parabolas
To convert into polynomial form:
FOIL the parenthesis
DISTRIBUTE (if necessary) the number outside
COMBINE like terms
Example: y = -2(x – 3)2 + 4
y = -2(x – 3)2 + 4
= -2(x – 3)(x – 3) + 4
= -2(x2 – 6x + 9) + 4
= -2x2 + 12x –
y = -2x2 + 12x – 14

7. 5-3: Translating Parabolas
Determine the y-intercept of the quadratic function and convert the function into polynomial form.
y = -3(x + 2)2 + 4
y-intercept:
Polynomial form:
y = (x – 3)2 – 4
y = -½(x – 2)2
(0, -8)
y = -3x2 – 12x – 8
(0, 5)
y = x2 – 6x + 5
(0, -2)
y = -½x2 + 2x – 2

8. 5-3: Translating Parabolas
Assignment
Page 251
Problems 1-11, odd
Ignore the directions!!!
Tell me:
Whether the graph opens up or opens down
The vertex
The y-intercept
The function written in polynomial form
Note: You may want to do part (d) before part (c)
Tomorrow, Practice with graphing
Friday, Quiz on 5-1 through 5-3