Question

Find the parabola with the equation \(y = ax^2 + bx\) whose tangent line at \((1, -1)\) has the equation \(y = 2x - 3\). What are the values of \(a\) and \(b\)? a) \(a = 1, b = -3\) b) \(a = 2, b = -1\) c) \(a = -1, b = 3\) d) \(a = -2, b = 1\)

Answer 1

Hi,

answer A

Explanation:

`y=ax^2+bx\\y'=2ax+b\\(1,-1)\ is\ a\ point\ of\ the\ parabola:\ a+b=-1\ (1)\\slope\ is \ 2\ at\ (1,-1):\ 2a=2\ \Longrightarrow\ \ a=1\ (2)\\\\\Longrightarrow\ b=-1-2*1=-3\\Answer:\ A\\`