# Finding unknown constants

• Sep 3rd 2012, 10:17 PM
Nora314
Finding unknown constants
Here is another problem from me.

I tried solving this, and I am thinking that I somehow need to turn this into an equation with some known points and than solve for a,b and c as a simultaneous equation. However, whenever I try to do this I get lost.

The curve y = ax2 + bx + c passes through the point (1; 2) and is tangent to the line
y = x at the origin. Find a, b and c

Thanks to everyone who reads this :)
• Sep 3rd 2012, 10:36 PM
MaxJasper
Re: Finding unknown constants
\$\displaystyle y=2x^2\$
• Sep 3rd 2012, 10:52 PM
JJacquelin
Re: Finding unknown constants
Hi !

"The curve y = ax² + bx + c is tangent to the line y = x at the origin"
To be tangent at the origin, at least the curve must pass through the point (0; 0). So 0=a^0+b*0+c. Hence c=0
y= ax²+bx.
The slope is y'(x)=2ax+b. The slope of the line y=x is 1. So, at the origine, 1=2*0+b. Hence b=1
y = ax²+1
The curve passes through the point (1; 2). So, 2=a*1²+1. Hence a=2-1=1
y = x²+x