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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

Respuesta :

Answer:

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

Step-by-step explanation:

We are given three points

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

We can verify each options

option-A:

[tex]y=x^2+6x+2[/tex]

we will verify each points

At (1,5):

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

[tex]y=(1)^2+6(1)+2[/tex]

[tex]y=9[/tex]

It does not satisfy point

So, this is FALSE

option-B:

[tex]y=x^2+6x-2[/tex]

we will verify each points

At (1,5):

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

[tex]y=(1)^2+6(1)-2[/tex]

[tex]y=5[/tex]

It satisfies point

At (-1,9):

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

[tex]y=(-1)^2+6(-1)-2[/tex]

[tex]y=-7[/tex]

It does not satisfy point

So, this is FALSE

option-C:

[tex]y=x^2-2x+6[/tex]

we will verify each points

At (1,5):

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

[tex]y=(1)^2-2(1)+6[/tex]

[tex]y=5[/tex]

It satisfies point

At (-1,9):

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

[tex]y=(-1)^2-2(-1)+6[/tex]

[tex]y=9[/tex]

So, it satisfies point

At (4,14):

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

[tex]y=(4)^2-2(4)+6[/tex]

[tex]y=14[/tex]

So, it satisfies point

so, this is TRUE


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