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 [tex]y \leq -3[/tex]
