Question

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

Answer 1

Below.

Explanation:

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

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

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

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

Then substitute `y = 0` to get

`0 = -(1/5)x^2`

Divide both sides by `1/5`

`0 = -x^2`

`sqrt0 = -x`

`0 = -x`

`x = 0`

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

Now substitute `x = 1`

`y = -(1/5)1^2`

`y = -(1/5)1`

`y = -(1/5)`

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

Now substitute `x = 2`

`y = -(1/5)2^2`

`y = -(1/5)4`

`y = -(4/5)`

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

Now you have 3 points: `(0,0), (1, -1/5),` and `(2, -4/5)` 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]}