Respuesta :

Answer:

[tex]f(x)=-0.5x^2+x+4[/tex]

Step-by-step explanation:

we know that

A quadratic function in factored form is equal to

[tex]f(x)=a(x-x_1)(x-x_2)[/tex]

where

a is the leading coefficient

x_1 and x_2 are the zeroes of the function

substitute the given values

[tex]f(x)=a(x-4)(x+2)[/tex]

Find the value of a

Remember that

For x=0 ----> f(0)=4

substitute

[tex]4=a(0-4)(0+2)[/tex]

[tex]4=a(-8)\\a=-0.5[/tex]

so

[tex]f(x)=-0.5(x-4)(x+2)[/tex]

[tex]f(x)=-0.5(x^2+2x-4x-8)[/tex]

[tex]f(x)=-0.5(x^2-2x-8)[/tex]

[tex]f(x)=-0.5x^2+x+4[/tex]

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