A quadratic is written in the form y= ax^2 +bx+c
Vertex form is known as y = a(x+b)^2 +c, giving the vertex as (-b,c)
It is useful to be able to change a quadratic expression into the form a(x+b)^2 +c. The process is by completing the square.
y =9x^2 +14x+12" "larr the coefficient of x^2 must be 1
y =9(x^2 +14/9x +12/9)
To make a square of a binomial, you need to add on color(blue)((b/2)^2)
It is also subtracted so that the value of the expression is not changed. color(blue)((b/2)^2 -(b/2)^2=0)
y =9(x^2 +14/9x color(blue)(+ (7/9)^2 -(7/9)^2) +12/9)
y = 9(color(red)((x^2 +14/9x + (7/9)^2))+color(green)(( -49/81 +12/9)))
y= 9(color(red)((x+7/9)^2 +color(green)((-49/81 12/9))))
y=9(x+7/9)^2+9(-49/81+108/81)
y = 9(x+7/9)^2 + 9(59/108))
y = 9(x+7/9)^2 +59/12
