Question

I still need help with similar question

Answer 1

Step-by-step explanation:

Step 1:  Determine the axis of symmetry

The axis of symmetry is middle of the parabola.  In this equation we see that at x = -1 we have the vertex and also the middle of the parabola.  So our axis of symmetry is x = -1.

Step 2:  Determine the vertex

The vertex is the minimum or maximum of a parabola and is bent in a crest form.  In this example the vertex is at (-1, -3) because we are using the tip of the graph.

Step 3:  Determine the y-intercept

The y-intercept is where the graph intersects with the y-axis.  In this example we intersect the y-axis at -4 so that means that our point would be (0, -4) meaning that we intersect x = 0 at -4.

Step 4:  Determine if the vertex is a min or max

Looking at the graph we can see that the rest of the red line is beneath the vertex point which means that the vertex is a max.

Step 5:  Determine the domain

The domain is the x-values that we are going to be using and we know that we are reaching toward positive and negative inifity which means that we are using all real numbers.

Step 6:  Determine the range

The range is the y axis and what y values we are able to reach using the graph.  In this example we can see that all y-values above -3 are not being used therefore the range is $y \leq -3$