Question

Select the correct answer. Which of these is the standard form of the following function? (f(t) = 7(-1)² + 3)

a. ( f(t) = 722 - 14t + 10 )
b. ( f(t) = -7.2 - 141 + 10 )
c. ( f(t) = 722 - 141 - 10 )
d. ( f(t) = -7t² - 141 - 10 )

Answer 1

The question seems to contain a typo as none of the answer choices correctly represent the standard form of the given constant function f(t) = 10. For a typical quadratic equation in the form at² + bt + c = 0, the quadratic formula is used to find the solutions for t.

Step-by-step explanation:

The initial function given by the student is f(t) = 7(-1)² + 3. Since (-1)² is 1, this simplifies to f(t) = 7(1) + 3, which further simplifies to f(t) = 10. This question seems to contain a typo, as none of the answer choices match a function that is simply a constant value like 10. Usually, a standard form of a quadratic function is at² + bt + c. However, to solve a quadratic equation using the quadratic formula, we need the equation to be in the form of at² + bt + c = 0.

If we consider another example quadratic equation t² + 10t - 200 = 0, the quadratic formula to find the values of t would be t = (-b ± √(b² - 4ac))/(2a). Applying the formula with a=1, b=10, and c=-200 would yield the solutions for t.