SOLUTION: what is the vertex of the quadratric equation y=x^2-6x+9

Question 1754: what is the vertex of the quadratric equation y=x^2-6x+9
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
firstly, how much maths do you know?
1. You could plot the graph and find the answer.
2. You can factorise the equation to sketch the graph.
3. You can differentiate the equation to sketch the graph.
I will assume you can do 1.
So, number 2...
Factorise..meaning 2 things multiplied. A quadratic will hopefully factorise into where a and b can be a positive or negative number or indeed can be the same number or more freaky, can by imaginary numbers... oh the joy of maths!
Anyway...a and b need to multiply together to give +9
and a and b need to add together to give -6.
So, what 2 numbers do that?
Answer...-3 and -3.
so, a=b=-3
so we have
Now, we sketch...by choosing some "obvious" points, namely when x=0 and when y=0.
So, when x=0...y=9
and when y=0...x=3.
Ta-da.

cheers
Jon.
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