Question

help please....The curve y = ax2 + bx + c is tangent to the line y = x in the origin. It is also tangent to the line y = 2x +3. Determine the function

Answer 1

f=ax^2 + bx + c
The derivative of the curve f'(x)=2ax+b
y=x is tangent to the curve in the origin, so at (0,0)
The means f(0)=0=a0^2+b0+c=c so c=0
b=1 because at the origin f'(0)=2*0+b=b (that is the slope of the tangent)
y=2x+3 is another tangent but we don't know where.
this line has slope 2 so we need to find where 2=f'(x)
2=2a+b (b=1)
2=2a+1, solving gives a=1/2
So the curve is
f(x)=1/2 x^2+x

Answer 2

ty

Answer 3

but where didi the x go in 2=2ax+b