SOLUTION: Complete the square to write each function in f(x) = a(x-h)^2 + k form. Determine the vertex and the axis of symmetry of the graph of the function. Then plot several points to comp

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Complete the square to write each function in f(x) = a(x-h)^2 + k form. Determine the vertex and the axis of symmetry of the graph of the function. Then plot several points to comp      Log On


   

Question 1084125: Complete the square to write each function in f(x) = a(x-h)^2 + k form. Determine the vertex and the axis of symmetry of the graph of the function. Then plot several points to complete the graph.
f(x) = x^2 - x - 6
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-x-6=0
x^2-x=6
x^2-x+1/4=6.25, add 1/4 to both sides. Get 1/4 by taking half of the x term and squaring it. That will allow one to complete the square.
(x-1/2)^2=6.25
(x-(1/2))^2-6.25=0
vertex is at (1/2, -6.25). One takes the value of x and changes the sign and the constant at the end keeps the sign and is the y-value.
axis of symmetry is at x=(1/2)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-x-6%2C%28x-0.5%29%5E2-6.25%29 This plots both x^2-x-6 and (x-0.5)^2-6.25

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square to write each function in f%28x%29+=+a%28x-h%29%5E2+%2B+k form. Determine the vertex and the axis of symmetry of the graph of the function.
Then plot several points to complete the graph.
f%28x%29+=+x%5E2+-+x+-+6
f%28x%29+=%28x%5E2+-+x+%2Bb%5E2%29-b%5E2-+6...since a=1 and 2ab=-1 we can determine b
2ab=-1->2%2A1%2Ab=-1->2b=-1->b=-1%2F2
f%28x%29+=%28x%5E2+-+x+%2B%28-1%2F2%29%5E2%29-%28-1%2F2%29%5E2-+6
f%28x%29+=%28x+-1%2F2%29%5E2-%281%2F4%29-+6
f%28x%29+=%28x+-1%2F2%29%5E2-%281%2F4%29-+24%2F4
f%28x%29+=%28x+-1%2F2%29%5E2-25%2F4
so, h=1%2F2 and k=-25%2F4->the vertex is at (1%2F2,-25%2F4)≈(0.5, -6.25)
The axis of symmetry of a parabola is the vertical line through the vertex.
so, axis of symmetry is x=1%2F2 or x=0.5

table:
x|y
-2|0....f%28-2%29+=+%28-2%29%5E2+-+%28-2%29-+6=4%2B2-6=0
-1|-4....f%28-1%29+=+%28-1%29%5E2+-+%28-1%29-+6=1%2B1-6=-4
0|-6....f%280%29+=+%280%29%5E2+-+%280%29-+6=0%2B0-6=-6
1|-6....f%281%29+=+%281%29%5E2+-+%281%29-+6=1-1-6=-6
2|-4....f%282%29+=+%282%29%5E2+-+%282%29-+6=4-2-6=-4
plot points and draw a graph: