I can't figure this out..

A physics student stands at the top of hill that has an elevation of 37 meters. He throws a rock and it goes up into the air and then falls back past him and lands on the ground below. The path of the rock can be modeled by the equation y = –0.02x² + 0.8x + 37 where x is the horizontal distance, in meters, from the starting point on the top of the hill and y is the height, in meters, of the rock above the ground. How far horizontally from its starting point will the rock land? Round your answer to the nearest hundredth
• 37.00 m
• 67.43 m
• 27.43 m
• 37.78 m

rock hits ground when y=0, so

-0.02x^2 + 0.8x + 37 = 0
x = 67.43

Thanks so much

To find the horizontal distance from the starting point where the rock will land, we need to find the value of x when y = 0. This is because when the rock lands on the ground, its height above the ground will be 0.

Given the equation y = –0.02x² + 0.8x + 37, we can set y equal to 0:
0 = –0.02x² + 0.8x + 37

Now, we need to solve this quadratic equation for x. We can use either factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = -0.02, b = 0.8, and c = 37. Plugging these values into the quadratic formula:
x = (-0.8 ± √(0.8² - 4(-0.02)(37))) / (2(-0.02))

Simplifying further:
x = (-0.8 ± √(0.64 + 2.96)) / (-0.04)
x = (-0.8 ± √3.6) / (-0.04)

Now we have two possible values for x, one using the positive square root and one using the negative square root. We can calculate these values using a calculator or approximations.

Using the positive square root:
x = (-0.8 + √3.6) / (-0.04) ≈ 27.43 meters

Using the negative square root:
x = (-0.8 - √3.6) / (-0.04) ≈ 37.78 meters

Since the rock is thrown from a starting point, we can discard the negative value for x. Therefore, the rock will land approximately 27.43 meters horizontally from its starting point.

So, the correct answer is:
• 27.43 m