Question

Identify all the points that are on the following quadratic function: y = x2 - 3x (0,3) (0,0) (2,-2) (-1,4) (-3,15)

Answer 1

B,C,D
Three answers. 2nd,3rd,4th

Answer 2

The points on the quadratic function
`y=x^(2)-3x` are :

`(0,0)`,
`(2,-2)` and
`(-1,4)`

Explanation:

We have the following quadratic function :

`y=x^(2)-3x`

If we want to see if a particular point is on the quadratic function we need to replace each pair
`(x,y)` in the quadratic function expression and check the equality.

For example :

We have the following point :
`(x,y)=(1,2)`

If we replace by
`x=1` and
`y=2` in the quadratic function :

`y=x^(2)-3x`

`2=1^(2)-3(1)`

`2=1-3`

`2=-2`

The final expression is false, therefore the point
`(1,2)` is not on the quadratic function.

Now let's work with the points we were given.

The first point is
`(0,3)` ⇒ If we replace in the quadratic function :

`y=x^(2)-3x`

`3=0^(2)-3(0)`

`3=0`

We conclude that the point
`(0,3)` is not in the quadratic function.

The second point is
`(0,0)`

`y=x^(2)-3x`

`0=0^(2)-3(0)`

`0=0`

This point is on the quadratic function.

The third point is
`(2,-2)`

If we replace in the quadratic function :

`y=x^(2)-3x`

`-2=(2)^(2)-3(2)`

`-2=4-6`

`-2=-2`

The point
`(2,-2)` is on the quadratic function.

The fourth point is
`(-1,4)`

`y=x^(2)-3x`

`4=(-1)^(2)-3(-1)`

`4=1+3`

`4=4`

Therefore the point
`(-1,4)` is on the quadratic function.

Finally, we have the point
`(-3,15)`

If we replace in the quadratic function :

`y=x^(2)-3x`

`15=(-3)^(2)-3(-3)`

`15=9+9`

`15=18`

This point is not on the quadratic function.

We conclude that the points
`(0,0),(2,-2)` and
`(-1,4)` are on the quadratic function
`y=x^(2)-3x`