Question

A curve has an x-intercept at * = 1. At its y-intercept of y = -3, the curve's tangent line

has a slope of -1. Find the equation of this curve in the form y

= ax2 + hx+c

Answer 1

$y=ax^2+bx+c\\y=0,x=1\Rightarrow a+b+c=0\\x=0,y=-3\Rightarrow c=-3\\y'\left( 0 \right) =b=-1\\\left\{ \begin{array}{c} a+b+c=0\\ c=-3\\ b=-1\\\end{array} \right. \Rightarrow a=4,b=-1,c=-3\\y=4x^2-x-3$