please check my answers.
2: how is the graph of y=-6x^2+4 different from the graph of y=6x^2
A: it is shifted 4 units to the left
B: it is shifted 4 units to the right
C: it is shifted 4 units up****
D:it is shifted 4 units down
3: A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation; y=-0.06x^2+9.6x+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 it's starting point will the rocket land? round your answer to the nearest hundredth
A: 4.30 m
B: 160.56 m****
C: 160.23 m
D: 13.94 m
both look good.
For question 2:
To determine how the graph of y = -6x^2 + 4 is different from the graph of y = 6x^2, we need to compare the coefficients and constants.
In the equation y = -6x^2 + 4, the coefficient in front of x^2 is -6. This negative coefficient indicates that the graph opens downward, forming a concave shape.
In contrast, the equation y = 6x^2 has a positive coefficient of 6 in front of x^2, indicating that the graph opens upward, forming a convex shape.
Therefore, the correct option is C: it is shifted 4 units up.
For question 3:
To determine how far horizontally from its starting point the rocket will land, we need to find the x-coordinate when the height (y) is equal to zero.
The equation y = -0.06x^2 + 9.6x + 5.4 represents the height of the rocket above the ground. We need to solve this equation for x when y = 0.
-0.06x^2 + 9.6x + 5.4 = 0
To find the x-values, we can either use the quadratic formula or factor the equation. In this case, factoring may not be straightforward, so let's use the quadratic formula.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation.
In this case, a = -0.06, b = 9.6, and c = 5.4.
x = (-9.6 ± √(9.6^2 - 4*(-0.06)*5.4)) / (2(-0.06))
Calculating this expression will give us two values for x. However, since the rocket is launched from a roof into a field, we only consider the positive value of x.
Calculating the expression, we find that x ≈ 160.56 meters.
Therefore, the correct answer is B: 160.56 m.