Yr.11 Stationary Points

[cheunga]

Hi, can someone please help me with this question, bearing in mind that this is at Yr.11 level so as dumbed down as possible a solution would be appreciated!  Thanks in advance.
The curve with equation y=ax²+bx+c has a stationary point at (1,2).  When x=0, the slope of the curve is 45^o.  Find a,b and c.

[Eric11267]

Hi, can someone please help me with this question, bearing in mind that this is at Yr.11 level so as dumbed down as possible a solution would be appreciated!  Thanks in advance.
The curve with equation y=ax²+bx+c has a stationary point at (1,2).  When x=0, the slope of the curve is 45^o.  Find a,b and c.

Okay so differentiating it gives you 2ax+b
At x=0 the slope is 45 degrees, which is a gradient of 1
So we have 2*a*(0)+b=1
b=1
Also at x=1 there is a turning point so the derivative equals 0
So we have 2a+1=0
a=-1/2
Finally putting the values of a and b back into the original equation and subbing in (1,2) gives c=3/2

[cheunga]

Hey Eric11267, thanks so much for your help! Much appreciated.

[Sigma]

Hey Eric 11267,

Thank you so much for your help. I was stuck on this question too. I also find these questions the most difficult. Dy/x a function and then subsiding in x to find y and thus giving you the coordinates for the local max and local min is easy - it is just these questions are always hard to answer. Finding 3 variables is hard considering it is only worth 3 marks. The first variable easy, it is the last two that are hard.

[Yueni]

I'd like to chime in here and say that the functional form you are given isn't necessarily the form you must do your working out in.

You are given a turning point, why not use turning point form for your quadratic? Then derive that and substitute x=0, dy/dx=1.
You can then expand your final quadratic to get a, b and c.

You save a little bit of time! And time is all so important when you never have enough of it.

[Sigma]

thanks for your help.

Eric11267's way is how the worked solutions do it and my teacher does it so I'll stick with that method. Thanks tho.