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The graph of a function f(x) passes through the following points:
(0,2), (1,0),(-1,0)
Which of the following could be f(x)?
O f(x) = - 2x2 + 2
O f(x) = 2x + 2
O f(x) = -27x + 2
O f(x) = - 2x + 2

Respuesta :

Answer:

All of the them excluding f(x)=-27x+2

The required function is [tex]f(x)=-2x^2+2[/tex]. Hence, option a is correct.

Important information:

  • The graph of a function passes through the points (0,2), (1,0) and (-1,0).

Quadratic function:

The graph has two x-intercepts (1,0) and (-1,0). It means it is a quadratic function and [tex](x-1)[/tex] and [tex](x+1)[/tex] are two factors.

[tex]f(x)=a(x-1)(x+1)[/tex]

[tex]f(x)=a(x^2-1)[/tex]         ...(i)

The graph passes through the point (0,2). Substitute [tex]x=0,f(x)=2[/tex] in the above function.

[tex]2=a(0^2-1)[/tex]

[tex]2=-a[/tex]

[tex]-2=a[/tex]

Substitute [tex]a=-2[/tex] in (i).

[tex]f(x)=-2(x^2-1)[/tex]

[tex]f(x)=-2x^2+2[/tex]

Therefore, the correct option is a.

Find out more about 'Quadratic function' here:

https://brainly.com/question/13965157

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