Quadratic Functions, Equations and Inequalities

Consider the function \(y=-x^2+4x+1.\)

1. Complete the table and draw the curve for \(-1\le x\le5\). Use a vertical range of \(-5\le y\le6\).

   \(x\)	\(-1\)	\(0\)	\(1\)	\(2\)	\( 3\)	\(4\)	\(5\)
   \(y\)

2. On the same axes, draw the straight line \(y=x+2. \)

   State two points used to draw the line. Read the \(x\)-coordinates of its intersections with the curve to \(1\) decimal place.

3. Show that your graphical answers solve \( x^2-3x+1=0. \)