find the equation of parabola with given two points B (2, 1) and C (4, 3) and slope of the tangent line to the parabola matches the slope of the line goes through A (0, 1.5) and B (2, 1).
i have calculated, that the slope for the line is -1/4. is it correct?
but i have no idea what the next step should be.
Any help would be appreciated.
Best Answer
To answer this problem, you must derive a system of linear equations to solve for the three unknowns in your parabola $f(x),$ where $$f(x)=ax^2+bx+c. $$ We know $f(2)=1=4a+2b+c$, $f(4)=3=16a+4b+c$, and $f'(\text{B})=-\frac{1}{4}=4a+b$. Thus, the system $$\begin{cases}4a+2b+c=1\\ 16a+4b+c=3\\ 4a+b=-\frac{1}{4} \end{cases} $$ is established. I will leave it up to you to solve for $f(x).$