Question

Sketch the graph of and identify the axis of symmetry

Answer 1

Answer:

Axis of symmetry is x = -4.

Step-by-step explanation:

The given equation is $y=-4(x+4)^2+4$

It represents a downward parabola because a = -4 <0

The vertex form of a parabola is

$y=a(x-h)^2+k$

Where (h,k) is the vertex and x = h is the axis of symmetry.

Thus, the vertex of the given parabola is (-4,4) and the axis of symmetry is x = -4.

The vertex will be at (-4,4) and is the lowest point of the graph of the parabola.

The x-intercept are

$0=-4(x+4)^2+4\\\\-4(x+4)^2=-4\\\\(x+4)^2=1\\\\x+4=\pm1\\\\x=-1-4,1-4\\\\x=-5,-3$

And the y-intercepts is

$y=-4(0+4)^2+4\\\\y=-4(16)+4\\\\y=-64+4\\\\y=-60$

Thus, using these facts we can draw the graph which is shown below.

Axis of symmetry is x = -4.

D is the correct option.

Answer 2

The axis of symmetry is found within the set of parenthesis with the x.  If our h value of the vertex is -4, then the axis of symmetry is x = -4.  D is that choice.  Cannot graph it here, but your vertex is sitting at (-4, 4), it's an upside down parabola, and some other points on this graph are (-5, 0), (-3, 0), (-6, -12), (-2, -12).  You could graph it using those points and the vertex without a problem, I'm sure.