Given that x^2 +ax +b =(x+2)^2 -9 work out a and b
expression x^2 - 10x - 5 can be written in form (x+p)^2 + q
find value of p and q
write expression 2x^2 - 8x + 19 in form a(x+b)^2 + c
find coordinates of minimum point on graph
state if and where the graph crosses x-axis
+128407 Given that x^2 +ax +b =(x+2)^2 -9 work out a and b
Just expand (x+2)^2 -9 =
x^2 + 4x + 4 - 9 = x^2 + 4x - 5 ⇒ a = 4 b = -5
x^2 - 10x - 5
Take 1/2 of 10 = 5.....square it = 25 .... add and subtract it
x^2 - 10x + 25 - 25 factor the first three terms
(x - 5)^2 - 25 = ( x + (-5) )^2 - 25 ⇒ p = -5 q = -25
write expression 2x^2 - 8x + 19 in form a(x+b)^2 + c
Factor out 2
2 [ x^2 - 4x + 19/2]
Take 1/2 of 4 = 2......square it......= 4.....add and subtract it
2 [ x ^2 - 4x + 4 + 19/2 - 4 ]
2 [ x^2 - 4x + 4 + 19/2 - 8/2 ] factor the first three terms
2 [ ( x - 2)^2 + 11/2]
2(x - 2)^2 + 11
The minimum point on the graph is (2,11)
Since this minimum lies above the x axis......the graph never crosses that axis
