Form quadratic functions given the following information:
f(3+√2 )=f(3− √2 )=0; f(1)=−8
The equation of the function is f(x) =?

or

Step-by-step explanation:

we have

f(3+√2 )=f(3− √2 )=0

so

x1=3+√2 and x2=3−√2 are the roots or x-intercepts of the quadratic equation

The quadratic equation in factored form is equal to

substitute

Find the value of the coefficient a

Remember that

f(1)=−8

so

For x=-1 -----> f(x)=-8

substitute

solve for a

apply difference of squares

therefore

simplify

Applying distributive property

(3x-8) or (3x+8)

step-by-step explanation: