How do you use the important points to sketch the graph of #y=-1/5x^2#?

Question

Eva Adamson · Accepted Answer

Below.

This graph is obviously just the parabola #y = x^2# transformed. graph{x^2 [-1, 10, 5, 5, -5]} First of all, it is an inverse parabola because #x^2# comes before a negative. graph{-x^2 [-10, 1, 5, 5, -5]} Next, change #y = 0# to obtain #0 = -(1/5)x^2# Split each side by #1/5#. #0 = -x^2# #sqrt0 = -x# #0 equals -x# #x equals 0# Thus, the initial key point #= (0,0)# Now replace #x = 1#. #y = -(1/5)1^2# #y = -(1/5)1# #y = -(1/5)# The subsequent crucial point is #= (1, -1/5)#. Substitute #x = 2# now. #y = -(1/5)2^2# #y = -(1/5)4# #y = -(4/5)# Thirdly, note that #= (2, -4/5)# Now that you have three points, #(0,0), #1, -1/5), and #(2, -4/5)#, you can use them to draw an inverse parabola on a graph because we know it's an inverse parabola. graph{-(1/5)x^2 [-10, 1, 5, 5, -10]}

Genesis Allen · Answer

undefined To sketch the graph of $ y = -\frac{1}{5}x^2 $, follow these steps:

1. Identify the vertex, which is the highest or lowest point on the graph.
2. Determine the direction of the opening of the parabola.
3. Plot the vertex on the graph.
4. Use the axis of symmetry to find additional points on the graph.
5. Plot additional points symmetrically around the axis of symmetry.
6. Draw a smooth curve passing through all plotted points to represent the graph of the equation.