Todd travels frequently for his business. For tax reasons, he wants to use up all of the remaining money in his business travel fund this year. He uses the function f(x)=x2−8x+16 to determine how many trips he must take to spend all of his remaining business travel funds. In this function, x represents the number of trips and f(x) is the amount of money left in his fund after the trips. The discriminant of this quadratic function tells us that this quadratic equation has (1 point) Responses no no one one two two three, according to this function, todd can use all of his remaining money in his travel fund if he takes ___ buisness trips this year.

Question

Todd travels frequently for his business. For tax reasons, he wants to use up all of the remaining money in his business travel fund this year. He uses the function f(x)=x2−8x+16 to determine how many trips he must take to spend all of his remaining business travel funds. In this function, x represents the number of trips and f(x) is the amount of money left in his fund after the trips. The discriminant of this quadratic function tells us that this quadratic equation has (1 point) Responses no no one one two two three, according to this function, todd can use all of his remaining money in his travel fund if he takes ___ buisness trips this year.

Answer 1

According to the function f(x) = x^2 - 8x + 16, Todd can use up all of his remaining money in his travel fund if he takes 4 business trips this year.

To determine this, we need to set the function equal to 0:
x^2 - 8x + 16 = 0

The discriminant of this quadratic function is b^2 - 4ac where a = 1, b = -8, and c = 16:
Discriminant = (-8)^2 - 4(1)(16) = 64 - 64 = 0

Since the discriminant is equal to 0, the quadratic equation has only one real root, meaning Todd can use up all of his remaining money in his travel fund by taking 4 business trips.