How do you tell whether the graph opens up or down, find the vertex and the axis of symmetry of #y=3(x+4)^2-2#?

2 Answers
Aug 26, 2017

See below.

Explanation:

When a quadratic is arranged in the form # a(x - h)^2 + k #
#k# is the minimum or maximum of the function.
#h# is the axis of symmetry.
From example:

vertex is #( -4 , -2) #
axis of symmetry is #- 4#

If #a# is negative, then the parabola is inverted i.e. #nnn#

If #a# is positive, then the parabola #uuu#

Aug 30, 2017

As the #x^2# term is positive the graph opens upwards

Vertex #->(x,y)=(-4,-2)#

So axis of symmetry is #x=-4#

Explanation:

If you expand the brackets and multiply by the three the first term is

#+3x^2#

As this is positive the graph is of general shape #uu#

Suppose it had been negative then in that case the graph would be of form #nn#

The given equation format is of type 'completing the square' also known as 'vertex form'.

#y=3(x+color(red)(4))^2color(blue)(-2)#

#x_("vertex")=(-1)xxcolor(red)(4) = -4#

#y_("vertex")=color(blue)(-2)#

Vertex #->(x,y)=(-4,-2)#

Tony B