SOLUTION: I'm struggling a lot with this one...I am so lost... Put equation in this form y=ax^2+bx+c Vertex (4, -1) passes through (2, 3)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I'm struggling a lot with this one...I am so lost... Put equation in this form y=ax^2+bx+c Vertex (4, -1) passes through (2, 3)      Log On


   

Question 927912: I'm struggling a lot with this one...I am so lost...
Put equation in this form y=ax^2+bx+c
Vertex (4, -1) passes through (2, 3)
Answer by Techpriest(29) About Me  (Show Source):
You can put this solution on YOUR website!
Did you remember the formula of:
+f%28x%29+=+a%28x-h%29%5E2%2Bk+
A vertex of this formula would be (h,k).
So we can plug in the vertex into this formula into:
+f%28x%29+=+a%28x-4%29%5E2-1+
We know that it passes through (2,3) so we can plug-in the x and y value into the formula also:
+3+=+a%282-4%29%5E2-1+
And so we combine like terms now.
+3+=+a%28-2%29%5E2-1+ Combine Like Terms
+3+=+4a-1+ Simplify
+3+%2B+1+=+4a-1%2B1+ Addition Property of Equality
+4%2F4+=+4a%2F4+ Division Property of Equality
+1+=+a+ Simplify
We know that a is one. So, into the formula we know that now.
+f%28x%29+=+1%28x-4%29%5E2-1+
+f%28x%29+=+%28x-4%29%5E2-1+ Distribution
+f%28x%29+=+x%5E2-8x%2B16-1+ FOIL
+f%28x%29+=+x%5E2-8x%2B15+ Simplify
+y+=+x%5E2-8x%2B15+ We know that f(x) is y.