so, the turning point is at
plug in and you will have 2 equations..
for the third equation:
a point is on the curve if and only if ..
The graph of the function y = ax≤ + bx + c has a turning point at (-3,2) and passes through the point (0,5). Determine the values of a, b and c.
I know this is only a basic question, but I really would appreciate your help.
You want the equation to pass through (0,5) so substitute x=0, y=5 into the equation to get y = 5 = c
You want the equation to pass through (-3,2) so substitute x=-3, y=2 into the equation to get
Then by knowing that at the turning point the differential of y with respect to x is zero you can write:
You have two equations in two variables which can be solved by symoltaneous equations.
since it passes through (0,5) this eq must satisfy it. So putting the values in the eq we get 5=a(0)^2+b(0)+c.which gives us c=5.
Now at turning point x=-b/2a
(if u wanna know why is it that so u may ask it in a new thread).since turning point is (-3,2) therefor x=-b/2a=-3 or b=6a. Substituting this value in eq we get y=ax^2+6ax+5 now substituting (-3,2) we get 2=9a-18a+5 or a=1/3 since b=6a therfor b=2.so finaly a=1/3,b=2,c=5
Now expand the turning point form to get the standard form.
Edit: Don't double post! It wastes peoples time! http://www.mathhelpforum.com/math-he...nt-thanks.html