Dear forum I have a question,
I need to Find the vertex of y = f(x) = 3x2 - 10x + 2 two different ways. What is the standard form of the equation?
any feed back would be appreciated..
The 'vertex' of a quadratic equation is a maxima or minima. You find this by differentiating the equation and setting the result equal to zero. You then solve this equation for x to give the x coordinate of the vertex. If you put this value back into the original equation, you find the y coordinate of the vertex.
$\displaystyle f(x) = 3x^2-10x+2 $
$\displaystyle f'(x) = 6x-10=0 $
$\displaystyle \therefore 6x=10 $
$\displaystyle \therefore x=\frac{10}{6} = \frac{5}{3} $
You could also find this minimum graphically I suppose. But that would probably rely on doing this process anyway.