# Vertex to Standard Form

```Vertex to Standard
Form
Notes
Change quadratic functions to standard form
2
y = (x +1) + 2
Rewrite (x+1)&sup2;
y = (x+1)(x+1)
Multiply using FOIL
2
y = x +x +x +1 +2
y = x2 +2x +3
2
y = ax +bx +c
Combine like terms
Standard Form
Compare Vertex vs. Standard
2
Vertex form: y = a (x - h) + k
2
Standard form: y = ax +bx +c
Lets look at our last problem
2
y = (x +1) + 2
y = x2 +2x +3
We converted to
a=1
h = -1
k=2
a=1
b=2
Compare values
c=3
You will learn that you will need to identify
the values for a, b, and c. Lets get into the
habit of identifying them NOW!!
Lets try this one!
Write the quadratic function in standard form.
Label the values for a, b, and c.
2
y = - (x + 3) +1
Steps:
Write (x+3) twice
Mulitply using Foil
Distribute the negative
like terms.
Write the quadratic function in standard form.
Label the values for a, b, and c.
2
2
y = 2 (x + 2)
y = -2 (x +1) + 3
2( x  2)( x  2)
2( x  2 x  2 x  4)
2
2 x2  4 x  4 x  8
2x  4x  4x  8
2
y  2 x  8x  8
2
2( x  1)( x  1)  3
Steps:
Write (
) twice
Mulitply using Foil
2( x 2  x  x  1)  3
2 x  2 x  2 x  2  3
2
Distribute number out front
Combine like terms.
y  2 x  4 x  1
2
Standard to Vertex
Step 1: Find x-coord x
y  2 x 2  8x  4
b

2a
8
x
 2
2(2)
Step 2: Plug x back into
equation to get y coord.
y  2(2)2  8(2)  4
y  8  16  4
Step 3: x and y are your
“h” and “k” in vertex
form
Step 4: “a” from
standard form is the
same “a” in vertex form
2
y = a (x - h) + k
y  4
Vertex: (-2, -4)
y  2( x  (2)) 2  (4)
y  2( x  2) 2  4
y  2x  4x  5
2
y  2( x  1) 7
2
y  x2  6 x  4
y  ( x  3)2  13
CLASSWORK/HOMEWORK
page 66 (25-27)
Problems on Agenda
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