How do you use the important points to sketch the graph of y=15x2?

1 Answer
Jun 11, 2018

Below.

Explanation:

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

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

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

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

Then substitute y=0 to get

0=(15)x2

Divide both sides by 15

0=x2

0=x

0=x

x=0

So the first major point =(0,0)

Now substitute x=1

y=(15)12

y=(15)1

y=(15)

The second important point =(1,15)

Now substitute x=2

y=(15)22

y=(15)4

y=(45)

The third important point =(2,45)

Now you have 3 points: (0,0),(1,15), and (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]}