How do you use the important points to sketch the graph of y=-1/5x^2y=15x2?

1 Answer
Jun 11, 2018

Below.

Explanation:

Clearly, this graph is just a transformation of the parabola y = x^2y=x2

graph{x^2 [-5, 5, -1, 10]}

The first thing to note is that there is a negative before x^2x2 so it is an inverse parabola

graph{-x^2 [-5, 5, -10, 1]}

Then substitute y = 0y=0 to get

0 = -(1/5)x^20=(15)x2

Divide both sides by 1/515

0 = -x^20=x2

sqrt0 = -x0=x

0 = -x0=x

x = 0x=0

So the first major point = (0,0)=(0,0)

Now substitute x = 1x=1

y = -(1/5)1^2y=(15)12

y = -(1/5)1y=(15)1

y = -(1/5)y=(15)

The second important point = (1, -1/5)=(1,15)

Now substitute x = 2x=2

y = -(1/5)2^2y=(15)22

y = -(1/5)4y=(15)4

y = -(4/5)y=(45)

The third important point = (2, -4/5)=(2,45)

Now you have 3 points: (0,0), (1, -1/5),(0,0),(1,15), and (2, -4/5)(2,45) and we know it's an inverse parabola so draw these points on a graph and then use them to draw an inverse parabola. And you get

graph{-(1/5)x^2 [-5, 5, -10, 1]}