What is the vertex form of #y= (x + 1)(x + 10) #?
1 Answer
Feb 21, 2016
Explanation:
The standard form of a quadratic function is
# y = ax^2 + bx + c # Before we get to vertex form , require to distribute the brackets.
hence (x + 1 )(x + 10 )
# = x^2 + 11x + 10# This is now in standard form and by comparison with
# ax^2 + bx + c# we obtain: a = 1 , b = 11 and c = 10
The vertex form of the equation is
# y =a (x - h)^2 + k #
where (h , k ) are the coords of vertex.x-coord of vertex (h)
# = (-b)/(2a) = -11/2 # and y-coord (k) =
#(-11/2)^2 + 11(-11/2) + 10 = 121/4 - 121/2 + 10 = -81/4#
hence a = 1 and (h , k )#= (-11/2 , -81/4 )#
#rArr y = (x + 11/2 )^2 - 81/4 #
