# SOLUTION: Any ideas here? Graph the function using the equation in part a (x2 - 6x + 8 = 0). Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k. Also,

Algebra ->  -> SOLUTION: Any ideas here? Graph the function using the equation in part a (x2 - 6x + 8 = 0). Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k. Also,       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Mathway solves algebra homework problems with step-by-step help!

Question 85410: Any ideas here?
Graph the function using the equation in part a (x2 - 6x + 8 = 0). Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k. Also, how would this graph compares to the graph of y = x2?

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 Distribute Multiply 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. Check: 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)

graph of (red) and the graph of (green) that has been shifted from the origin