This is very similar to a previous post, so I just borrowed the graphic from the member call Shiraz (hope you don't mind)

The parabola is modeled by the quadratic equation y=ax^2+bx+c
a) Write three equations to find the values of a,b and c.
b) Solve the equations in (a) to find the equation of the parabola, use exact values.
c) Hence, show point B has a gradient of zero.

There's a lot more of this project I can't do so I may ask for more help after this, but for now thank you in advance for anyone willing to have a look.

2. Originally Posted by Supernova
This is very similar to a previous post, so I just borrowed the graphic from the member call Shiraz (hope you don't mind)

The parabola is modeled by the quadratic equation y=ax^2+bx+c
a) Write three equations to find the values of a,b and c.
b) Solve the equations in (a) to find the equation of the parabola, use exact values.
c) Hence, show point B has a gradient of zero.

There's a lot more of this project I can't do so I may ask for more help after this, but for now thank you in advance for anyone willing to have a look.
Hint:

$\left\{\!\begin{gathered}0=0\cdot{a}+0\cdot{b}+c,\hfill\\30=30^2a+30b+c,\hfill\\40=60^2a+60b+c;\hfill\\\end{gathered}\right.~\Leftrightarrow~\left\{\!\begin{gathered}a=-1/90,\hfill\\b=4/3,\hfill\\c=0.\hfill\\\end{gathered}\right.$

3. This is more than a little similar to another post. I'd say it was pretty nearly identical.