Questions on Algebra: Graphs, graphing equations and inequalities answered by real tutors!

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Question 168083: The vertex of a quadratic function is (-5,-3) and the graph of the function contains the point (1,2). Is this enough information to determine the equation of the function? if so, give the equation of the function. if not explain why.
: The vertex of a quadratic function is (-5,-3) and the graph of the function contains the point (1,2). Is this enough information to determine the equation of the function? if so, give the equation of the function. if not explain why.

Answer by jojo14344(1022) About Me  (Show Source):
You can put this solution on YOUR website!
Given the vertex (-5,-3) at points (1,2):
We can solve the eqn. using the Vertex Form in Solving Quadratic:
f(x)=a(x-h)^2+k
f(x)=a(x-(-5))^2+(-3)
f(x)=a(x+5)^2-3
2=a(x^2+10x+25)-3
2=a(1^2+10*1+25)-3
2=36a-3
2+3=36a
cross(36)a/cross(36)=5/36 --->a=5/36
It follows the eqn:f(x)=(5/36)x^2+(5/36)10x+(5/36)(25)
f(x)=(5/36)x^2+(50/36)x+(125/36)-3
f(x)=(5/36)x^2+(25/18)x+(125-108)/36
highlight(f(x)=(5/36)x^2+(25/18)x+(17/36)), ANSWER
See graph:
drawing(300,300,-20,10,-6,10,grid(1),graph(300,300,-20,10,-6,10,(5/36)x^2+(25/18)x+(17/36)),circle(-5,-3,.25),circle(1,2,.25))) ----> See vertex (-5,-3) with points (1,2)
Thank you,
Jojo