Question

The graph of the curve $x^2=3x-y-2$, is

• A. between the lines $x=1$ and $x=\frac{3}{2}$
• B. between the lines $x=1$ and $x=2$
• C. strictly below the line $4y=1$
• D. none of these

Answer 1

The correct option is C strictly below the line $4y=1$

$x^2=3x-y-2$
by rearranging that equation we get $-(x^2-3x+2)=y$
the maximum value of the curve is $\frac{1}{4}$ (maximum value is $-\frac{\Delta }{4a}$)
So it always lies below $\frac{1}{4}$.