f(x) is a quadratic function whose graph passes through (2,9) and (0,1).If the gradient of the graph at x=2 is 6, find f(x)
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f(x) is a quadratic function whose graph passes through (2,9) and (0,1).If the gradient of the graph at x=2 is 6, find f(x)
solve? well, duh! Why else post the question?
f(x) = ax^2 + bx + c
f'(x) = 2ax+b
since f'(2) = 6,
4a+b = 6
Now, using the two points, we also have
4a+2b+c = 9
c = 1
solving those 3 equations, we get
f(x) = x^2 + 2x + 1 = (x+1)^2
f(x) = ax^2 + bx + c
f'(x) = 2ax+b
since f'(2) = 6,
4a+b = 6
Now, using the two points, we also have
4a+2b+c = 9
c = 1
solving those 3 equations, we get
f(x) = x^2 + 2x + 1 = (x+1)^2