Question

The path of a basketball thrown at an angle of 45° can be modeled by y=-0.02x²+x+6 , where x is the horizontal distance (in feet) and y is the vertical distance (in feet).

Find and interpret the coordinates of the vertex. The coordinates of the vertex are 25 , 18.5 |). When the basketball is at its highest point, it is feet from its starting point and feet off the ground.

Answer 1

The coordinates of the vertex are (25, 18.5). When the basketball is at its highest point, it is 25 feet from its starting point and 18.5 feet off the ground.

Step-by-step explanation:

The path of a basketball thrown at an angle of 45° can be modeled by the equation y = -0.02x² + x + 6, where x is the horizontal distance and y is the vertical distance.

To find the coordinates of the vertex, we need to find the x-coordinate of the vertex using the formula

x = -b/2a, where a, b, and c are the coefficients of the equation.

In this case,

a = -0.02 and

b = 1.

Plugging in these values, we get

x = -1/(2 * -0.02)

= 25.

Now, to find the y-coordinate, we substitute this value into the equation:

y = -0.02 * 25² + 25 + 6

= 18.5.

The coordinates of the vertex are (25, 18.5). When the basketball is at its highest point, it is 25 feet from its starting point and 18.5 feet off the ground.