How do you determine the vertex and direction when given a quadratic function?

1 Answer
Nov 24, 2014

There are two forms a quadratic function could be written in: standard or vertex form. Here are the following ways you can determine the vertex and direction dependent on the form:

Standard Form (#f(x)=ax^2 + bx + c#)
1. Direction of the parabola can be determined by the value of a. If a is positive, then the parabola faces up (making a u shaped). If a is negative, then the parabola faces down (upside down u).
2. Vertex can be found by #x= -b/(2a)# and then plugging in that value to find y.
Here is an example:
#y = -2x^2 + 4x - 3#, Faces downward since a = -2.
to find the vertex: #x= (-4)/(2(-2))=(-4)/ (-4) = 1#
then plug that value into the equation#y = -2x^2 + 4x - 3#
#y = -2(1)^2 + 4(1) - 3 #
#y = -2(1) +4(1) - 3 #
#y = -2 + 4 -3 #
#y = -1 #
Vertex is (1,-1)

Vertex Form (#y=a(x-h)^2 +k#)
1. Direction of the parabola can be determined by the value of a. If a is positive, then the parabola faces up (making a u shaped). If a is negative, then the parabola faces down (upside down u).
2. Vertex is (h,k).
Here is an example:
#y = -3(x-2)+6# Faces down since a = -3 and the vertex is (2, 6).