You can put this solution on YOUR website!
I'm assuming you want to convert
into vertex form right?
|Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form|
Start with the given equation
Subtract from both sides
Factor out the leading coefficient
Take half of the x coefficient to get (ie ).
Now square to get (ie )
Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation
Now factor to get
Now add to both sides to isolate y
Combine like terms
Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.
Notice if we graph the original equation we get:
Graph of . Notice how the vertex is (,).
Notice if we graph the final equation we get:
Graph of . Notice how the vertex is also (,).
So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.
If a=1, which it does, then we only need the vertex coordinates to plot the graph of
. Simply plot the vertex at (3,-1)
Starting at the vertex, go to the right one unit and up 1 unit and plot (4,0). Go back to the vertex and go to the left one unit and up 1 unit and plot (2,0).
Now that you have 3 points, you can draw a parabola through them.
This is the quick and easy way to graph parabolas
Since a=1, the graph of
has the same shape as
. The only difference is the vertex of
has been shifted 3 units to the right and one unit down. In other words,
has a vertex at (0,0) and to get
, simply move the graph
to the point (3,-1)
(red) and the graph of
(green) that has been shifted from the origin