Chapter 2 - Differentiation - 2.2 Exercises - Page 117: 111

$y=2x^2-3x+1$

$y=ax^2+bx+c$ Passes through $(0,1)$, $(1)=a(0)^2+b(0)+c$ $c=1$ $y=ax^2+bx+1$ It also passes through (1,0), $y=ax^2+bx+1$ $(0)=a(1)^2+b(1)+1$ $a+b=-1$ $\frac{dy}{dx}=2ax+b$ Tangent to $y=x-1$ at $(1,0)$ The tangent has a slope of $1$ when $x=1$ $2a(1)+b=1$ $2a+b=1$ $2a+b=1$ $a+b=-1$ Subtracting both equations yields, $a=2$. $(2)+b=-1$ $b=-3$ $y=ax^2+bx+1$ $y=2x^2-3x+1$