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Form quadratic functions given the following information:
Zeroes at 4 and –2, f(0)=4

1 Answer

5 votes

Answer:


f(x)=-0.5x^2+x+4

Explanation:

we know that

A quadratic function in factored form is equal to


f(x)=a(x-x_1)(x-x_2)

where

a is the leading coefficient

x_1 and x_2 are the zeroes of the function

substitute the given values


f(x)=a(x-4)(x+2)

Find the value of a

Remember that

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

substitute


4=a(0-4)(0+2)


4=a(-8)\\a=-0.5

so


f(x)=-0.5(x-4)(x+2)


f(x)=-0.5(x^2+2x-4x-8)


f(x)=-0.5(x^2-2x-8)


f(x)=-0.5x^2+x+4

User Surajd
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