Identify the x-intercepts of y = −4.9x^2 − 9.8x + 5 using the quadratic formula,
To find the x-intercepts of the quadratic equation y = -4.9x^2 - 9.8x + 5, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -4.9, b = -9.8, and c = 5.
Plugging these values into the quadratic formula, we get:
x = (-(-9.8) ± √((-9.8)^2 - 4(-4.9)(5))) / (2(-4.9))
Simplifying, we have:
x = (9.8 ± √(96.04 + 98)) / (-9.8)
x = (9.8 ± √(194.04)) / (-9.8)
x = (9.8 ± 13.94) / (-9.8)
Now we have two possibilities:
1. x = (9.8 + 13.94) / (-9.8)
x = 23.74 / (-9.8)
x ≈ -2.426
2. x = (9.8 - 13.94) / (-9.8)
x = -4.14 / (-9.8)
x ≈ 0.422
Therefore, the x-intercepts of the equation y = -4.9x^2 - 9.8x + 5 are approximately -2.426 and 0.422.