Question

Please help with these three questions

Answer 1

Explanation:

44). Given function is,

f(x) = 7x² - 3x - 1

x intercept means value x at f(x) = 0.

Therefore, for f(x) = 0

7x² - 3x - 1 = 0

By quadratic formula,

x =
`(-b\pm √(b^2-4ac) )/(2a)`

=
`(3\pm √((-3)^2-4(7)(-1)))/(2(7))`

=
`(3\pm √(37))/(14)`

Therefore, x - intercepts are x =
`(3- √(37))/(14),(3+√(37))/(14)` ≈ -0.22, 0.65

45). f(x) = x² + 4x + 7

For x intercepts, f(x) = 0

x² + 4x + 7 = 0

By quadratic formula,

x =
`(-4\pm √(16-28))/(2)`

=
`(-4\pm √(-12) )/(2)`

= (-2 ± i
`√(12)`)

Since, x intercepts are imaginary, there are no x-intercepts.

46). Given formula for the projectile is,

s = 96t - 16t²

For s = 96 ft

96 = 96t - 16t²

6 = 6t - t²

0 = -t² + 6t - 6

t² - 6t + 6 = 0

By quadratic formula,

t =
`(6\pm √(6^2-4(1)(6)))/(2(1))`

t =
`(6\pm √(36-24))/(2)`

t =
`(6\pm √(12) )/(2)`

t = (3 ± √3) ≈ 1.27 seconds, 4.73 seconds