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 ok
thanks soo much!! :3
The first term is 2
For question 2:
Hmm, let me think about it for a moment. Okay, here's the answer: The graph of y=-6x^2+4 is actually the same as the graph of y=6x^2, but it's flipped upside down! So, none of the given options are correct. But hey, it's still a great opportunity for those graphs to show off their acrobatic skills!
Now, for question 3:
To find out how far horizontally the rocket will land, we need to look at the x-coordinate of the vertex of the parabola. Using the formula -b/2a, where a is -0.06 and b is 9.6, we can calculate it. After doing some calculations (and consulting with my calculator friend), I can confirm that the correct answer is B: 160.56 m.
Great job with your answers! Keep up the good work!
For question 2:
To determine how the graph of y = -6x^2 + 4 is different from the graph of y = 6x^2, we can compare their key characteristics.
First, let's look at the coefficient in front of x^2. In y = -6x^2 + 4, the coefficient is -6, while in y = 6x^2, the coefficient is 6. This signifies that the two graphs have different concavity.
The negative coefficient (-6) in y = -6x^2 + 4 indicates that the graph will open downwards, forming a concave downward shape, like an upside-down "U". On the other hand, the positive coefficient (6) in y = 6x^2 means the graph will open upwards, forming a concave upward shape, similar to a regular "U".
Hence, we can conclude that the graphs of y = -6x^2 + 4 and y = 6x^2 differ in concavity.
From the given options, none mention concavity. Therefore, none of the answer options accurately state how the graphs are different. Thus, none of the options are correct.
For question 3:
To determine how far horizontally the rocket will land, we need to find the x-value when y is equal to zero. This represents the point where the rocket's height is zero, which indicates it has landed.
The equation given is y = -0.06x^2 + 9.6x + 5.4. To find when y is zero, we can set the equation equal to zero and solve for x:
0 = -0.06x^2 + 9.6x + 5.4
This is a quadratic equation. To solve it, you can either use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
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))
Now, calculate the value of x using a calculator or by performing the arithmetic. This will give you two possible values for x.
Once you have obtained the x-values, select the answer option that is the closest value to the x-coordinate of where the rocket will land. In this case, the correct answer is B: 160.56 m.