The graph of y = x2 is shown below. Using complete sentences, explain how the graph

Question

The graph of y = x2 is shown below. Using complete sentences, explain how the graph
of y = -2(x + 3)2 + 1 would differ from this parabola?

 

The graph shows a parabola opening up with a vertex at 0 comma 0

Answer 1

To solve this problem, you have to break down the equation into parts and figure out how each piece affects the picture.  It is a good idea to use the point-slope formula which is y=a(x-h)²+k and break it down by variable.

 

a: This is the slope.  Since this slope is negative, the parabola will be facing down.  With a slope of 2, the parabola will be much narrower because it is covering 2 vertical blocks to 1 horizontal block on the grid, therefore it will be twice as tall as it is wide.

(h,k) is the vertex of the parabola or the point that is in the middle (in this case it is the highest point on the parabola since the parabola is facing downward).

 

h: -3 represents the vertex being three blocks to the left of the origin with regards to the x-axis.

 

k: 1 represents that the vertex is one block above the origin with regards to the y-axis.