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.
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
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
To compare these two functions, let's look at the general form of a quadratic function: y = ax^2 + bx + c.
The first given function is y = -8x^2 - 2, and the second given function is y = -8x^2.
The only difference between these two functions is the constant term. In the first function, the constant term is -2, while in the second function, it is 0.
The constant term affects the vertical position of the graph because it represents a vertical shift. When the constant term is positive, it shifts the graph upwards, and when it is negative, it shifts the graph downwards.
In this case, the constant term in the first function is negative (-2), so the graph is shifted downward compared to the graph of the second function. It is not shifted to the left or right.
Therefore, the correct answer is D. It is shifted 2 units down.