Write the equation of the quadratic function with roots 0 and 1 and a vertex at (1/2,-2/3)

Question

anonymous · Answer

@Traxter can you help?

anonymous · Answer

Sure, the equation has roots 0 and 1, so will look something like this:
$$y=ax(x-1)$$
For some x which we need to find.
Now, you have a corresponding set of x and y values which you can plug into the above equation to find the required a.
Are you able to have a go at the next bit yourself or do you need a hand?

anonymous · Answer

Also are you comfortable with why the equation has the form which I have put it in?

anonymous · Answer

i need a hand :/

anonymous · Answer

Ok, substitute x=1/2 and y=-2/3 to get:
$$-2/3 = \frac{a}{2}\times(-\frac{1}{2})$$
$$\frac{-2}{3}=\frac{-a}{4}$$
Multiply by -4 to get:
$$a=\frac{8}{3}$$
So the equation will be:
$$y=\frac{8x}{3}(x-1)$$
Do you understand?

anonymous · Answer

Also, if you expand it will be:
$$y=\frac{8x^2}{3}-\frac{8x}{3}$$

anonymous · Answer

thank you traxter :))

anonymous · Answer

Not a problem :)