Question

What is the equation, in standard form, of a parabola that contains the following points? (1,5), (-1,9), (4,14)

A) y=x^2+6x+2
B) y=x^2+6x-2
C) y=x^2-2x+6
D) y=x^2-2x-6

Answer 1

C) y=x^2-2x+6

Explanation:

We are given three points

(1,5) (-1,9) and (4,14)

We can verify each options

option-A:

`y=x^2+6x+2`

we will verify each points

At (1,5):

we can plug x=1 and check whether y=5

`y=(1)^2+6(1)+2`

`y=9`

It does not satisfy point

So, this is FALSE

option-B:

`y=x^2+6x-2`

we will verify each points

At (1,5):

we can plug x=1 and check whether y=5

`y=(1)^2+6(1)-2`

`y=5`

It satisfies point

At (-1,9):

we can plug x=-1 and check whether y=9

`y=(-1)^2+6(-1)-2`

`y=-7`

It does not satisfy point

So, this is FALSE

option-C:

`y=x^2-2x+6`

we will verify each points

At (1,5):

we can plug x=1 and check whether y=5

`y=(1)^2-2(1)+6`

`y=5`

It satisfies point

At (-1,9):

we can plug x=-1 and check whether y=9

`y=(-1)^2-2(-1)+6`

`y=9`

So, it satisfies point

At (4,14):

we can plug x=4 and check whether y=14

`y=(4)^2-2(4)+6`

`y=14`

So, it satisfies point

so, this is TRUE