How do you tell whether the graph opens up or down, find the vertex, and find the axis of symmetry given #y=-2x^2-6x+3#?

1 Answer
Feb 21, 2018

Opens Down
Vertex: (-#3/2#, #15/2#)
Axis of Symmetry: x=-#3/2#

Explanation:

So one of the easiest ways you can find this information is by graphing. The axis of symmetry will always be a vertical line for a quadratic equation, so it will always be x= (x value of the vertex)

Let's start from the basics,

Standard form, a#x^2#+bx+c

The a value determines whether the parabola is face up or down. A negative 'a' value, such as -2, makes the parabola open down, whereas a positive 'a' value like 2, will make the parabola open up.

To find the vertex of a quadratic function, first calculate #(-b)/(2a)# to find the 'x' value of the vertex.

So #(-(-6))/(2(-2))#, gives you #-3/2#. This is the x value of the vertex. And you can then determine the axis of symmetry from here which is x= #-3/2#

Now for the 'y' value of the vertex, simply substitue #x# with #-3/2# and solve.

So, -2 #(-3/2)^2#-6(#-3/2#)+3

This simplified gives you -#9/2#+ 9 + 3
Add the numbers together, and you should get #15/2#

So your vertex is (-#3/2#, #15/2#)

Hope this clarifies things!