Answer:
A. (-1, -4)
Step-by-step explanation:
The vertex can be found by converting the equation from standard form to vertex form.
<h3>Vertex</h3>
Considering the x-terms, we have ...
y = (x^2 +2x) -3
where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...
y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2
y = (x +1)^2 -4
Compare this to the vertex form equation ...
y = a(x -h)^2 +k
which has vertex (h, k).
We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).
On the attached graph, the vertex is the turning point, the minimum.
As go up the number sequence it is just the number added to get the new number plus 1. For example, since 2+3=5, 5+3=8+1=9
First find the slope of the line segment joining the points.
Slope = ((-5)-7)/(1-(-3)) = -3
The slope of any perpendicular to the line is 1/3
Find the midpoint of the line segment by taking the average of the coordinates.
x-coord of midpoint = (-3+1)/2 = -1
y-coord of midpoint = (7-5)/2 = 1
Midpoint : (-1,1)
Point-slope equation for line of slope 1/3 that passes through (-1,1):
y-1 = (1/3)(x+1)