How is the graph of y equals negative 8x squared minus 2. different from the graph of y equals negative 8x squared.?
A. It is shifted 2 units to the left.
B.
It is shifted 2 units to the right.
C.
It is shifted 2 units up.
D.
It is shifted 2 units down.
3 answers
D. It is shifted 2 units down.
A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y equals negative 0.06 x squared plus 9.6 x plus 5.4 where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.
How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.
A. 4.30 m
B. 160.56 m
C. 161.12 m
D. 13.94 m
How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.
A. 4.30 m
B. 160.56 m
C. 161.12 m
D. 13.94 m
To find where the rocket lands, we need to find the value of x when y = 0 (since the rocket will be at ground level at that point).
0 = -0.06x² + 9.6x + 5.4
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = -0.06, b = 9.6, and c = 5.4.
Plugging in these values, we get:
x = (-9.6 ± √(9.6² - 4(-0.06)(5.4))) / 2(-0.06)
Simplifying:
x = (-9.6 ± √(9.6² + 1.296)) / (-0.12)
x ≈ -6.34 or x ≈ 160.56
We can disregard the negative value, since we're looking for a distance. Therefore, the rocket will land approximately 160.56 meters horizontally from its starting point.
Rounding to the nearest hundredth:
Answer: C. 161.12 m
0 = -0.06x² + 9.6x + 5.4
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = -0.06, b = 9.6, and c = 5.4.
Plugging in these values, we get:
x = (-9.6 ± √(9.6² - 4(-0.06)(5.4))) / 2(-0.06)
Simplifying:
x = (-9.6 ± √(9.6² + 1.296)) / (-0.12)
x ≈ -6.34 or x ≈ 160.56
We can disregard the negative value, since we're looking for a distance. Therefore, the rocket will land approximately 160.56 meters horizontally from its starting point.
Rounding to the nearest hundredth:
Answer: C. 161.12 m