Answer:
[tex](x - 1)^2 - 6[/tex]
Step-by-step explanation:
You need to know:
Vertex form = [tex]a(x -h)^2 + k[/tex]
The vertex is at
(h, k)
Need to know about perfect squares
Need to know how to complete the square.
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To convert [tex]x^2-2x-5[/tex] you need to complete the square on the equation.
Complete the Square [tex]x^2 - 2x -5[/tex]
[tex]x^2 - 2x -5[/tex]
[tex](x^2 - 2x) -5[/tex]
Divide -2 by 2 and then square it.
[tex]\frac{-2}{2} = -1[/tex]
[tex]-1^2 = 1[/tex]
Add the one to the parentheses and subtract the one from the 5
[tex](x^2 - 2x +1) -5 -1[/tex]
Square [tex](x^2 - 2x +1)[/tex]
[tex](x-1)^2[/tex]
Now we have
[tex](x - 1)^2 -5 -1[/tex]
Next add -5 - 1 = -6
[tex](x - 1)^2 - 6[/tex]
Our quadratic is in vertex form now.
Vertex form = [tex]a(x -h)^2 + k[/tex]
our equation = [tex](x - 1)^2 - 6[/tex]
Vertex = (1, -6)
