A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.02x2 + 2.3x + 6, 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? My mind is blank...

57.50 m
115.00 m
117.55 m
235.10 m

Its 117.55 ^^

bro thanks

i guess it still works for the future highschool students 2023,2024,2025,2026,2027,2028,2029

Well, it sounds like you need a little boost to get your mind out of the blank zone! Don't worry, with a little rocket science (of the non-serious kind), I can help you out!

To find out how far horizontally the rocket will land, we need to determine the value of x when y reaches 0. In other words, we need to find the x-intercept of the equation y = –0.02x^2 + 2.3x + 6.

Now, don't let those intimidating numbers scare you! Just remember, math is like taking off with a rocket – you need to break it down step by step!

To find the x-intercept, we set y to 0 and solve for x. So, let's set up our equation:

0 = –0.02x^2 + 2.3x + 6

Now, take a deep breath, summon your mathematical powers, and let's solve it!

Unfortunately, my humor sensors are detecting some serious math vibes here, so I'll give you the answer straight: the rocket will land approximately 115.00 meters horizontally from its starting point.

There you have it! I hope my little comedic touch helped lighten up the rocket science! Safe travels to the rocket, and keep exploring the world of math!

To find 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. This is because the rocket will land on the ground when its height is zero.

So, we have the equation y = -0.02x² + 2.3x + 6.

To solve for x when y is equal to zero, we set the equation equal to zero:

0 = -0.02x² + 2.3x + 6.

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.

However, in this case, it's easier to solve using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

For our equation -0.02x² + 2.3x + 6, a = -0.02, b = 2.3, and c = 6.

Plugging in these values into the quadratic formula, we get:

x = (-2.3 ± √(2.3² - 4*(-0.02)*6)) / (2*(-0.02)).

Simplifying further, we have:

x = (-2.3 ± √(5.29 + 0.48)) / (-0.04),

x = (-2.3 ± √5.77) / (-0.04).

Now, we have two possible solutions for x: one with a positive sign and one with a negative sign. However, since we are looking for the horizontal distance, it must be a positive value. Thus, we can ignore the solution with the negative sign.

Calculating the positive solution:

x = (-2.3 + √5.77) / (-0.04),

x ≈ 57.50 m.

Therefore, the rocket will land approximately 57.50 meters horizontally from its starting point.

The correct answer is 57.50 m.

it lands when the height (y) is zero. So, just solve for x in

-0.02x2 + 2.3x + 6 = 0

just use the quadratic formula.