What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function #y = - x^2- 4x + 3#?

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Answer 1 · 2016-01-14T09:30:39

Vertex: #(-2,7)#
Axis of symmetry: # x=-2#
Maximum value : #7#
Domain: #(-oo,oo)#
Range: #(-oo,7]#

We are given a quadratic function #y=-x^2-4x+3#

On graphing it would graph a parabola.

Since the coefficient of #x^2# is negative the parabola would be open down.

The #x# coordinate of vertex would help in finding the axis of symmetry.

For the graph which opens down, there is only maximum and that can be found by the #y# coordinate of the vertex.

So first let us find the vertex. There are many different approaches to find the vertex.

Let us try one method.

To find the vertex #(h,k)# we can use the following.

#h=-b/(2a)# and #k= y(h)#

#h=-(-4)/(2(-1))#

#h=4/-2#

#h=-2#

#k=-(-2)^2-4(-2)+3#
#k=-4+8+3#

#k=7#

Vertex: #(-2,7)#
Axis of symmetry: # x=-2#
Maximum value : #7#
Domain: #(-oo,oo)#
Range: #(-oo,7]#

Check the graph to understand it.

graph{y=-x^2-4x+3 [-10, 10, -5, 8]}