This topic focuses on practicing the skill of converting quadratic equations from standard form to vertex form by completing the square. Each problem presents a different quadratic equation, and the task involves finding the vertex of each equation after transforming it into vertex form. The exercises are designed to enhance understanding of quadratic transformations, specifically focusing on manipulating the equations to reveal the vertex, which is a crucial aspect in graph plotting and analysis of quadratic functions. This topic is part of a broader unit on quadratic equations and their vertex forms.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Quadratic Equation Standard Form to Vertex (Coefficient N) Worksheet

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Quadratic Equation Standard Form to Vertex (Coefficient N)
1
Complete the square and convert this to vertex form to find the vertex
A LaTex expression showing y=2x to the power of 2 +4x+3
a
(1, -1)
b
(2, -1)
c
(1, 1)
d
(-1, 1)
e
(2, 1)
f
(-1, -1)
2
Complete the square and convert this to vertex form to find the vertex
A LaTex expression showing y=4x to the power of 2 -16x+12
a
(2, -4)
b
(2, 4)
c
(-2, -4)
d
(-4, 2)
e
(4, -4)
f
(4, 2)
3
Complete the square and convert this to vertex form to find the vertex
A LaTex expression showing y=4x to the power of 2 -24x+39
a
(4, 3)
b
(-3, 3)
c
(3, 3)
d
(3, -3)
4
Complete the square and convert this to vertex form to find the vertex
A LaTex expression showing y=5x to the power of 2 +10x+4
a
(5, -1)
b
(-1, 1)
c
(1, -1)
d
(-1, -1)
5
Complete the square and convert this to vertex form to find the vertex
A LaTex expression showing y=5x to the power of 2 -40x+81
a
(4, -1)
b
(4, 1)
c
(-4, 1)
d
(1, 4)
e
(5, 4)
f
(5, 1)
6
Complete the square and convert this to vertex form to find the vertex
A LaTex expression showing y=5x to the power of 2 -40x+83
a
(5, 3)
b
(3, 4)
c
(4, 3)
d
(5, 4)
e
(4, -3)
f
(-4, 3)
7
Complete the square and convert this to vertex form to find the vertex
A LaTex expression showing y=5x to the power of 2 +40x+76
a
(5, -4)
b
(-4, 4)
c
(-4, -4)
d
(4, -4)
8
Complete the square and convert this to vertex form to find the vertex
A LaTex expression showing y=3x to the power of 2 +6x+4
a
(3, -1)
b
(1, 1)
c
(-1, -1)
d
(-1, 1)
e
(1, -1)
f
(3, 1)