Name: _______________________
Non Factorable Quadratics – Vertex Form
Try Now:
Part A The graph of 𝑓(𝑥) = 𝑥 2 + 6𝑥 + 9 is shown
below.
Date: ___________
Algebra I Common Core
Sheet # 17-10
Part B The graph of 𝑔(𝑥) = −𝑥 2 + 4𝑥 − 1 is shown
below.
What is the vertex of the graph? ____________
What is the vertex of the graph? ____________
Is this a minimum or a maximum? ___________
Is this a minimum or a maximum? ___________
Write the perfect square trinomial 𝑥 2 + 6𝑥 + 9 in
factored form.
After completing the square the function is written as
𝑔(𝑥) = −(𝑥 − 2)2 + 3.
We can get the vertex form by completing the square.
#’s 1- 8: Given the function in vertex form, determine the vertex and state whether it is a min or max.
1
2
3
𝑓(𝑥) = (𝑥 − 2)2 − 3
4
𝑓(𝑥) = 7(𝑥 − 1)2 + 2
7
𝑓(𝑥) = −(𝑥 + 4)2 + 5
Vertex: ___________
Vertex: ___________
Vertex: ___________
Max/Min? _________
Max/Min? _________
Max/Min? _________
𝑓(𝑥) = −2(𝑥 + 3)2 − 4
5
𝑓(𝑥) = (𝑥 + 0)2 − 9
8
𝑓(𝑥) = −(𝑥 − 1)2 + 2
Vertex: ___________
Vertex: ___________
Vertex: ___________
Max/Min? _________
Max/Min? _________
Max/Min? _________
𝑓(𝑥) = 3(𝑥 + 6)2 − 7
6
𝑓(𝑥) = (𝑥 − 8)2
Vertex: ___________
Vertex: ___________
Max/Min? _________
Max/Min? _________
HACK!!!
#’s 9-12: Given the vertex, state one possible function for the graph in vertex form. The first one is done for you.
9
11 (6, −7), max
10 (6, 7), min
12 (−6, −7), min
Regents Multiple Choice Problems
13
If Jacky completes the square for
𝑓(𝑥) = 𝑥 2 + 10𝑥 − 4 in order to find the
minimum, she must write 𝑓(𝑥) in the general
form 𝑓(𝑥) = (𝑥 − 𝑎)2 + 𝑏. What is the value of
a for 𝑓(𝑥)?
(1) 5
15
In the function 𝑓(𝑥) = (𝑥 − 4)2 + 3, the
minimum value occurs when x is
(1) -3
(3) 3
(2)
-4
(4)
4
Calculator Hack!!!
(2) 10
(3) -5
(4) -10
16
14
If Roman completes the square for
𝑓(𝑥) = 𝑥 2 − 12𝑥 + 7 in order to find the
minimum, he must write 𝑓(𝑥) in the general
form 𝑓(𝑥) = (𝑥 − 𝑎)2 + 𝑏. What is the value of
a for 𝑓(𝑥)?
(1) 6
(2) -6
(3) 12
(4) -12
In the function 𝑓(𝑥) = (𝑥 + 6)2 − 2, the
minimum value occurs when x is
(1) -2
(3) -6
(2)
17
2
(4)
6
Which equation and ordered pair represent the
correct vertex form and vertex for
𝑗(𝑥) = 𝑥 2 − 10𝑥 + 9 ?
(1) 𝑗(𝑥) = (𝑥 − 5)2 − 16,
(5, −16)
(2)
𝑗(𝑥) = (𝑥 − 5)2 − 16,
2
(−5, −16)
(3)
𝑗(𝑥) = (𝑥 − 5) + 34,
(5, 34)
(4)
𝑗(𝑥) = (𝑥 − 5)2 + 34,
(−5, 34)
Calculator Hack!!!
Name: _______________________
Non Factorable Quadratics – Vertex Form
Date: ___________
Algebra I Common Core
Calculator Hacks!
1 Given the function below, state whether the
vertex represents a maximum or minimum
point for the function. Explain your reasoning.
𝑓(𝑥) = 𝑥 2 + 4𝑥 − 1
Sheet # 17-11
If you are stuck on a problem like this you can use your
calculator to help you get a lot of points.
To determine max or min, look at graph.
If you find the vertex first using the table of values, it will
be easy to write the answer in vertex form.
Rewrite 𝑓(𝑥) in vertex form by completing
the square.
Check that your equation is correct by comparing it to
the original table of values. They should match.
What point represents the vertex?
What if they do not match??? This will happen if the
coefficient of 𝑥 2 is not 1. Simply write a in front of the
parenthesis.
Examples:
Function: 𝑓(𝑥) = −𝑥2 − 4𝑥 + 1
Vertex: (−2, 5)
Vertex Form: 𝑓(𝑥) = −(𝑥 + 2)2 + 5
Function: 𝑓(𝑥) = 5𝑥 2 + 20𝑥 + 7
Vertex: (−2, −13)
Vertex Form: 𝑓(𝑥) = 5(𝑥 + 2)2 − 13
2
Given the function below, state whether the
vertex represents a maximum or minimum
point for the function. Explain your
reasoning.
𝑓(𝑥) = 𝑥 2 + 12𝑥 + 40
4
Rewrite 𝑓(𝑥) = −𝑥 2 − 14𝑥 + 15 in vertex
form by completing the square.
State the vertex.
5
Rewrite 𝑓(𝑥) = 2𝑥 2 + 12𝑥 + 16 in vertex
form by completing the square.
State the vertex.
6
Rewrite 𝑓(𝑥) = 3𝑥 2 − 18𝑥 + 12 in vertex
form by completing the square.
State the vertex.
Rewrite 𝑓(𝑥) in vertex form by completing
the square.
What point represents the vertex?
3
Given the function below, state whether the
vertex represents a maximum or minimum
point for the function. Explain your
reasoning.
𝑓(𝑥) = −𝑥 2 − 2𝑥 − 3
Rewrite 𝑓(𝑥) in vertex form by completing
the square.
What point represents the vertex?