Question

Solve the quadratic expression -16t² + 4t + 4 and round your answer to the nearest hundredth.

Answer 1

0.64 and -0.39

Step-by-step explanation:

-16t^2+4t+4 = 0

delta = 16+256 =272

this means t = (-4+-sqrt272)/-32 = (-4+-4sqrt17)/-32 = (-1+-sqrt 17)/-8

if t = (-1-sqrt17)/-8 this means we get with aproxmiation 0.64. if t = (-1+sqrt 18)/-8 we get with approximation -0.39

Answer 2

The solutions to the quadratic expression -16t² + 4t + 4, rounded to the nearest hundredth, are approximately t ≈ 0.38 and t ≈ 0.62.

Step-by-step explanation:

To solve the quadratic expression -16t² + 4t + 4, we can use the quadratic formula t = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic expression in the form ax² + bx + c. In this case, a = -16, b = 4, and c = 4. Plugging these values into the quadratic formula, we get t = (-4 ± √(4² - 4(-16)(4))) / (2(-16)). Simplifying further, we get t ≈ (-4 ± √160) / -32, which results in the solutions t ≈ 0.38 and t ≈ 0.62.

The rounded solutions to the nearest hundredth are t ≈ 0.38 and t ≈ 0.62. These values represent the points where the quadratic expression equals zero. It's essential to round to the nearest hundredth to provide a more manageable and precise representation of the solutions. The process of solving quadratic equations using the quadratic formula is a fundamental skill in algebra and has various applications in mathematics and science. The solutions indicate the x-intercepts of the quadratic function and provide valuable information about its behavior.