Question

Kiara tosses a coin off a bridge into the stream below. The quadratic regression equation can be found using the following ordered pairs, where y is the height (in feet) and x is the time (in seconds). Use the following ordered pairs to create the quadratic regression equation: (0, 112), (2, 240), (5, 192), (7,0). What is the maximum height of the coin?

Answer 1

To find the maximum height of the coin, we need to determine the vertex of the quadratic regression equation. We can use the given ordered pairs to create a system of equations and solve for the coefficients. Finally, substitute the x-value of the vertex into the equation to find the maximum height of the coin.

Step-by-step explanation:

To find the maximum height of the coin, we need to determine the vertex of the quadratic regression equation. The quadratic regression equation is of the form y = ax² + bx + c, where a, b, and c are constants. We can use the given ordered pairs to create a system of equations:

Using the equation x = -b/2a, we can find the x-coordinate of the vertex. Plugging this value into the equation y = ax² + bx + c will give us the maximum height of the coin.

By substituting the values from the given ordered pairs into the quadratic regression equation, we can solve the system of equations to find the values of a, b, and c.

After finding the coefficients, we can substitute the x-value of the vertex into the equation to find the maximum height of the coin.