SOLUTION: Please HELP me with this Quadratic Function. Sketch the graph of f(x)=-x2+6x-8. Indentity the vertex and x-intercepts. f(x)=-x2+6x-8 =-(x2-6)-8 =-(x2-6x+9-9)-8 (I don

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please HELP me with this Quadratic Function. Sketch the graph of f(x)=-x2+6x-8. Indentity the vertex and x-intercepts. f(x)=-x2+6x-8 =-(x2-6)-8 =-(x2-6x+9-9)-8 (I don      Log On


   

Question 80103: Please HELP me with this Quadratic Function. Sketch the graph of
f(x)=-x2+6x-8. Indentity the vertex and x-intercepts.
f(x)=-x2+6x-8
=-(x2-6)-8
=-(x2-6x+9-9)-8 (I don't understand how you get 9.It said to Factor -1 out of x-terms. I get stuck at that point. I know how to graph it.)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form


y=1+x%5E2%2B6+x-8 Start with the given equation



y%2B8=1+x%5E2%2B6+x Add 8 to both sides



y%2B8=1%28x%5E2%2B6x%29 Factor out the leading coefficient 1



Take half of the x coefficient 6 to get 3 (ie %281%2F2%29%286%29=3).


Now square 3 to get 9 (ie %283%29%5E2=%283%29%283%29=9)





y%2B8=1%28x%5E2%2B6x%2B9-9%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 9 does not change the equation




y%2B8=1%28%28x%2B3%29%5E2-9%29 Now factor x%5E2%2B6x%2B9 to get %28x%2B3%29%5E2



y%2B8=1%28x%2B3%29%5E2-1%289%29 Distribute



y%2B8=1%28x%2B3%29%5E2-9 Multiply



y=1%28x%2B3%29%5E2-9-8 Now add %2B8 to both sides to isolate y



y=1%28x%2B3%29%5E2-17 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=-3, and k=-17. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=1x%5E2%2B6x-8 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2%2B6x-8%29 Graph of y=1x%5E2%2B6x-8. Notice how the vertex is (-3,-17).



Notice if we graph the final equation y=1%28x%2B3%29%5E2-17 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x%2B3%29%5E2-17%29 Graph of y=1%28x%2B3%29%5E2-17. Notice how the vertex is also (-3,-17).



So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.