Question

What is the x-intercept h=-16t^2+20t+6?​

Answer 1

see explanation

Explanation:

To find the intercepts equate h to zero, that is

- 16t² + 20t + 6 = 0 ← divide all terms by 2

- 8t² + 10t + 3 = 0 ← multiply through by - 1

8t² - 10t - 3 = 0 ← factor the quadratic

Consider the factors of the product of the coefficient of the t² term and the constant term which sum to give the coefficient of the t- term

product = 8 × - 3 = - 24 , sum = - 10

Factors are - 12 and + 2

Use these factors to split the middle term

8t² - 12t + 2t - 3 = 0 ( factor the first/second and third/fourth terms )

4t(2t - 3) + 1(2t - 3) = 0 ← factor out (2t - 3)

(2t - 3)(4t + 1) = 0

Equate each factor to zero and solve for t

2t - 3 = 0 ⇒ 2t = 3 ⇒ t =
`(3)/(2)`

4t + 1 = 0 ⇒ 4t = - 1 ⇒ t = -
`(1)/(4)`

Intercepts are (-
`(1)/(4)`, 0) abd (
`(3)/(2)`, 0)