Subject: Algebra
Created by: Matthias Fisseha
Revised: 07/09/2018
Standard (Vertex) Form
What is standard (vertex) form of a quadratic function?
- Vertex form is a way to rewrite a quadratic function in a way that the vertex can be
identified easily.
- The standard (vertex) form is as follows: f(x) = a(x-h)
2
+k, where (h, k) is the vertex of the
function and a is the quadratic coefficient.
How can a quadratic function be rewritten in vertex form?
- A quadratic function can be rewritten in vertex form by completing the square.
- The following is an example:
f(x) = x
2
-2x-8 The given function is in the form f(x) = ax
2
+bx +c form.
f(x) = (x
2
-2x) -8 First, group the x
2
and x terms.
f(x) = (x
2
-2x+1) -8-1 Then, add (b/2)
2
inside the parentheses and subtract the same
value on the outside.
f(x) = (x-1)(x-1) -9 Next, factor the expression in the parentheses and combine
like terms.
f(x) = (x-1)
2
-9 Finally, simplify. The vertex is (1, -9).
- Here is another example that is a bit more complicated:
f(x) = (x-1)
2
-9
(1,-9)
Subject: Algebra
Created by: Matthias Fisseha
Revised: 07/09/2018
Standard (Vertex) Form
f(x) = -2x
2
-8x+13 The given function is in the form f(x) = ax
2
+bx +c form.
f(x) = (-2x
2
-8x) +13 First, group the x
2
and x terms.
f(x) = -2(x
2
+4x ) + 13 Factor out any common numbers.
f(x) = -2(x
2
+4x+4) + 13 -4(-2) Then, add (b/2)
2
inside the parentheses and subtract
the same value on the outside. This time, when
subtracting by (b/2)
2
on the outside, multiply it by the
number that was factored out.
f(x) = -2(x+2)(x+2) +13+8 Next, factor the expression in the parentheses and
multiply.
f(x) = -2(x+2)
2
+21 Finally, simplify. The vertex is (-2, 21).
You Try!
-Try rewriting the following functions in standard (vertex) form:
f(x) = 3x
2
-12x-3
f(x) = -6x
2
+18x-9
--
The following works were referred to during the creation of this handout: Wolfram Alpha.
f(x) = -2(x+2)
2
+21
(-2, 21)
