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Finding the Vertex of a Parabola by Completing the Square  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
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.
Graphing a parabola when you're not dealing with vertex form. So we know how to graph a parabola when we are in vertex form and we know what these transformations are. This k is going to move the graph up and down, this h is going to move everything side to side and this a is just going to affect the direction and the shape, how steep or narrrow our parabola is.
The problem is when we have something in standard form, x squared minus 4x+6. We don't know how to deal with these transformations, so what we have to do is somehow take this quadratic equation and put it into this form, and how we do that is by completing the square.
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Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
Sample Problems (8)
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Finding the Vertex of a Parabola by Completing the Square
Problem 1 7,837 viewsFind the vertex of:
y = x² − 4x + 6 
Finding the Vertex of a Parabola by Completing the Square
Problem 2 5,769 viewsFind the vertex of:
f(x) = 2x² + 8x + 3 
Finding the Vertex of a Parabola by Completing the Square
Problem 3 4,520 viewsFind the vertex of:
f(x) = ½x² + 3x + 4 
Finding the Vertex of a Parabola by Completing the Square
Problem 4 576 views 
Finding the Vertex of a Parabola by Completing the Square
Problem 5 613 views 
Finding the Vertex of a Parabola by Completing the Square
Problem 6 497 views 
Finding the Vertex of a Parabola by Completing the Square
Problem 7 612 views 
Finding the Vertex of a Parabola by Completing the Square
Problem 8 656 views
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