Putting Functions Into Vertex Form Worksheet
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5Name:__________________________________
Algebra 2
January 23 (A Block), January 24 (E Block), 2014
Putting Functions into Vertex Form
As a reminder, here’s a quadratic function in vertex form: f(x) = a(x – h)
2
+ k. The vertex is at
(h, k), and the a value tells the parabola’s direction ( if a > 0, if a < 0).
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How to put f(x) = ax
+bx+c into vertex form
Method 1: Completing the Square
– 18x + 23 into vertex form, and identify the vertex.
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Put the function f(x) = 3x
First move the c value to the other side just like you do when equation solving
f(x) – 23 = 3x
– 18x
2
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Next, factor out the 3 from the x
and x terms:
f(x) – 23 = 3(x
– 6x)
2
– 6x + ? . As before, the needed
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Think about how to complete the perfect square: x
– 6x + __9__. So we want to insert a 9 inside the
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number is found by halving and squaring: x
parentheses.
Now here’s the crucial step: inserting a 9 would increase the function’s value by 9·3=27.
So, we need to offset this increase by adding 27 to the other side.
f(x) – 23 + 27 = 3(x
– 6x + 9)
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Write the perfect square as a square, and combine the – 23 +27 to get:
f(x) + 4 = 3 (x – 3)
2
.
Finally, subtract the four from both sides to get:
f(x) = 3 (x – 3)
– 4
vertex: (3, –4)
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Method 2: Find the Vertex
Put the function f(x) = –2x
– 20x + 10 into vertex form, and identify the vertex.
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-b
Find the vertex by using our formula x =
2a
-(-20)
20
x =
=
= -5
-4
2(-2)
This is the x-coordinate. Plug into the function to find y:
– (20)(-5) +10 = -50 +100 + 10 = 60
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f(-5) = (-2)(-5)
vertex: (–5, 60)
Plug the vertex into vertex form, keeping the a value from standard form:
f(x) = –2(x + 5)
2
+ 60
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