Amery recorded the distance and height of a basketball when shooting a free throw.
1. Find the quadratic equation for the relationship of the horizontal distance and the height of the ball. Round to 3 decimal places.
2. Using this function what is the approximate maximum height if the ball?
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trajectory
To find the quadratic equation representing the relationship between the horizontal distance and the height of the ball, you will need two data points with both the distance and height values.
Let's assume Amery recorded two data points:
- (x1, y1) = (distance1, height1)
- (x2, y2) = (distance2, height2)
Using these data points, we can apply the quadratic equation:
Step 1: Define the variables
- x represents the horizontal distance.
- y represents the height of the ball.
Step 2: Write the equation
The quadratic equation has the general form of y = ax^2 + bx + c.
Step 3: Substitute the data points into the equation
We have two equations based on the given data points:
1) y1 = a(x1)^2 + b(x1) + c
2) y2 = a(x2)^2 + b(x2) + c
Step 4: Solve the equations simultaneously
By solving the above two equations simultaneously, you can find the values of a, b, and c.
Once you find the values of a, b, and c, you will have the quadratic equation representing the relationship between the horizontal distance and the height of the ball.
Now, to determine the approximate maximum height of the ball, you can use the equation for maximum height given by h = -b/(2a), where h is the maximum height.
Using the quadratic equation obtained from the previous steps, substitute the values of a and b into the maximum height equation and solve for h.
To find the quadratic equation for the relationship between the horizontal distance and the height of the ball, you will need at least three data points. If you provide the data points, I can help you find the quadratic equation.
Once we have the quadratic equation, we can determine the approximate maximum height of the ball using the vertex form of the equation. Please provide the necessary data points so I can assist you further.