Question

If f (x)=x^2-1 which of the following ordered pairs are on the graph of f(x)

Answer 1

(1,0)

(5,24)

(-2,3)

Explanation:

we have

`f(x)=x^(2)-1`

This is the equation of a vertical parabola open upward

Remember that

If a ordered pair is on the graph of the quadratic equation, then the ordered pair must satisfy the quadratic equation

Verify each case

case A) we have

(0,1)

Substitute the value of x and the value of y in the quadratic equation

`1=0^(2)-1`

`1=-1` ----> is not true

therefore

The ordered pair is not on the graph of f(x)

case B) we have

(1,0)

Substitute the value of x and the value of y in the quadratic equation

`0=1^(2)-1`

`0=0` ----> is true

therefore

The ordered pair is on the graph of f(x)

case C) we have

(3,5)

Substitute the value of x and the value of y in the quadratic equation

`5=3^(2)-1`

`5=8` ----> is not true

therefore

The ordered pair is not on the graph of f(x)

case D) we have

(5,24)

Substitute the value of x and the value of y in the quadratic equation

`24=5^(2)-1`

`24=24` ----> is true

therefore

The ordered pair is on the graph of f(x)

case E) we have

(-2,3)

Substitute the value of x and the value of y in the quadratic equation

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

`3=3` ----> is true

therefore

The ordered pair is on the graph of f(x)

case F) we have

(-4,-17)

Substitute the value of x and the value of y in the quadratic equation

`-17=-4^(2)-1`

`-17=15` ----> is not true

therefore

The ordered pair is not on the graph of f(x)

using a graphing tool

see the attached figure to better understand the problem