1. Converting Between Standard Form and Vertex Form
Unit 4 - Quadratics

2. Two Forms of a Quadratic
y = ax2 + bx + c
a = # in front of x2
b = # in front of x
c = # without a variable
c is always the y- intercept
Can be graphed by a table of values, finding the vertex, or by graphing calculator
y = a(x – h)2 + k
a is the # in front of x2
h is the x-value of the vertex
k is the y-value of the vertex
(h, k) represents the vertex
Can be graphed by transformations
Standard Form
Vertex Form

3. Converting From Standard Form to Vertex Form
To convert from Standard Form y = ax2 + bx + c to Vertex Form y = a(x – h)2 + k you must find the vertex using x = -b/2a
x = -b/2a finds the x-value of the vertex, which is h.
Then you plug the x-value you found into the equation in standard form to find the y-value of the vertex.
The a comes from the # in front of the x2.
Now rewrite the equation using the values of h, k, and a in vertex form.

4. Example 1: Convert from standard form to vertex form: y = 3x2 + 6x - 1
Use x = -b/2a
a = 3, b = 6
x = -6/2(3)
x = -6/6
x = -1, which means h = - 1
We know x = -1, so we plug that into the standard form
y = 3(-1)2 + 6(-1) – 1
y = 3(1) + 6(-1) – 1
y = 3 – 6 – 1
y = -3 – 1
y = -4, which means k = -4
To Find the x-value (h)
To Find the y-value (k)

5. Writing Out the Final Answer
k = -4
a = 3
y = a(x – h)2 + k
y = 3(x – (-1))2 – 4
y = 3(x + 1)2 – 4

6. You Try 1: Convert from standard form to vertex form: y = -2x2 + 12x – 12
Use x = -b/2a
a = -2, b = 12
x = -12/2(-2)
x = -12/-4
x = 3, which means h = 3
We know x = 3, so we plug that into the standard form
y = -2(3)2 + 12(3) – 12
y = -2(9) + 12(3) – 12
y = – 12
y = 18 – 12
y = 6, which means k = 6
To Find the x-value (h)
To Find the y-value (k)

7. Writing Out the Final Answer
k = 6
a = -2
y = a(x – h)2 + k
y = -2(x – (3))2 + 6
y = -2(x - 3)2 + 6

8. Converting From Vertex Form to Standard Form
To convert from Vertex Form y = a(x – h)2 + k to Standard Form y = ax2 + bx + c you must simplify the vertex form of the equation by following ORDER OF OPERATIONS.
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction

9. Example 2: Convert from vertex form to standard form: y = 4(x – 2)2 + 3
First step is to square (x – 2)
(x – 2)(x – 2)
x2 – 2x – 2x + 4
x2 – 4x + 4
Second step is the distribute 4
4(x2 – 4x + 4)
4x2 – 16x + 16
Third step is to add 3
y = 4x2 – 16x This is the final answer