I like the way geno did this one.......however..... what if we forgot (or didn't know) that the x coordinate of the vertex occurs mid-way between the roots?? Here's an alternative approach - though maybe not as "neat"
We have
0 = a(10)^2 + b(10) + c
0 = a(34)^2 + b(34) + c
Subtracting the first equation from the second, we get
0= a(34^2 - 10^2) + b(34 - 10) simplify
0 = a(1056) + b(24) rearrange
-b(24) = a(1056) divide both sides by 24
-b = a(44) = 44a
Now.....suppose that we do remember that the x coordinate of the vertex is given by
x = -b / 2a so we have
x = 44a / 2a = 22 .....and that's the x coordinate of the vertex
And now we can continue the problem just as geno did by finding the value of "a," etc. !!!
