Finding the Vertex of a Parabola by Completing the Square - Concept

Concept Concept (1)

In order to graph a parabola, we need to find several pieces of information, including the vertex. One way to find the vertex of a parabola is to turn the standard form of the quadratic equation into vertex form by completing the square. The primary difference between solving a quadratic by completing the square and putting an equation into vertex form is substituting a "y" for the "0" in the initial equation.

Sample Sample Problems (8)

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Finding the Vertex of a Parabola by Completing the Square - Problem 1

Find the vertex of:

y = x² − 4x + 6
Problem 1
How to find the vertex of a parabola by completing the square.
Finding the Vertex of a Parabola by Completing the Square - Problem 2

Find the vertex of:

f(x) = -2x² + 8x + 3
Problem 2
How to find the vertex of a parabola by completing the square with a negative leading coefficient.
Finding the Vertex of a Parabola by Completing the Square - Problem 3

Find the vertex of:

f(x) = ½x² + 3x + 4
Problem 3
How to find the vertex of a parabola by completing the square with a fractional leading coefficient.
Finding the Vertex of a Parabola by Completing the Square - Problem 4
Problem 4
Using completing the square to change from standard to vertex form when "a" is not one and "b" is even
Finding the Vertex of a Parabola by Completing the Square - Problem 5
Problem 5
Changing a parabola from standard to vertex form without completing the square
Finding the Vertex of a Parabola by Completing the Square - Problem 6
Problem 6
Using completing the square to change from standard to vertex form when "a" is not one and "b" is odd
Finding the Vertex of a Parabola by Completing the Square - Problem 7
Problem 7
Using completing the square to change a quadratic equation from standard for vertex form when "a" is one and "b" is even
Finding the Vertex of a Parabola by Completing the Square - Problem 8
Problem 8
Using completing the square to change a quadratic equation from standard for vertex form when "a" is one and "b" is odd