Question

Rewrite the following quadratic functions in intercept or factored form. Show your work.

f(t) = 20t^2 + 14t - 12

Answer 1

f(t) = 2(2t - 1)(5t + 6)

Explanation:

We are given a quadratic equation and we have to convert it into factored from. For this purpose we will do factorization.

f(t) = 20t^2 + 14t - 12

first take 2 as common from the right hand side of equation

f(t) = 2(10t² + 7t - 6)

We can break the midterm (+7t) in two terms such that when they are multiplied the result is -60 i.e. equal to product of first and third term of the equation above.

`f(t) = 2(10t^(2)+12t-5t-6)\\ \\ f(t) = 2(2t(5t+6)-1(5t+6))`

Taking 5t+6 as common above

f(t) = 2(2t - 1)(5t + 6)