Example 8
Express -2x2+4x+4 in the form a(x-h)2+k. Hence, i) Sketch the graph
of -2x2+4x+4
Example 9
Example 10
Example 11
Samson thre# a all sch that the height, s metres, of the all at
time t seconds is gi"en y the e'ation s$-4.t2+"t+*., #here " ms is
the speed at #hich he thre# the all /se the discriminant, i) &o
determine #hether the all
cold reach a height of * m if it is thro#n at a speed of *0ms
ii) &o sho# that "20.1 if the
&he natre of the roots to the 'adratic e'ation
ax2+x+c$% determines #hether the graph y$ ax2+x+c intersects the
x-axis.
Discriminant and %ntersection
&he sign of the discriminant also determines #hether a
'adratic graph intersects a straight line.
3 %
$ %
Example 12
Example 13
a) Sho# that y$x2-2x+4 is positi"e for all real "ales of x
Example 14
Example 15
a) 7etermine #hether the line y$2x+ intersects the cr"e
y$4x2+:
Example 16
&o sol"e a 'adratic ine'ality graphically, follo# these
steps9
Example 17
Example 18
=i"en the cr"e y$2x2-mx+2, ;nd the range of "ales of m i) !or #hich
the e'ation y$% has
real roots ii) 5f the line y$2-x intersects the
cr"e at t#o distinct points
