Question

A ball is thrown upward and outward from a height of 6 feet. The table shows four measurements indicating the ball's height at various horizontal distances fromwhere it was thrown. A graphing calculator displays a quadratic function that models the ball's height, y, in feet, in terms of its horizontal distance, x, in feet. Answerparts (a)-(c) below.x, Ball's Horizontal Distance (feet) y, Ball's Height (feet)06QuadRegy=ax²2+bx+ca=-1.0b=2.917.962.24c = 6.0T(x) = -1.0x + 2.9x+6.0c. Use the model from part (b) to determine the x-coordinate of the quadratic function's vertex.3

Answer 1

The x-coordinate of the vertex is 1.5

The maximum height of the ball occurs 1.5 feet from where it was thrown and the maximum height is 8.1 feet

Step-by-step explanation:

In an equation of the form y = ax² + bx + c, the x-coordinate of the vertex is x = -b/2a.

In this case, the equation is y = -1.0x + 2.9x + 6.0. So, a = -1.0 and b = 2.9. It means that the x-coordinate of the vertex is

x = -b/2a

x = -2.9/2(-1.0)

x = -2.9/(-2)

x = 1.5

Now, we can find the value of y replacing x = 1.45, so

y = -1.0x² + 2.9x + 6.0

y = -1.0(1.5)² + 2.9(1.5) + 6.0

y = -1.0(2.25) + 4.35 + 6.0

y = -2.25 + 4.35 + 6.0

y = 8.1

It means that when the horizontal distance is 1.5 feet, the height is 8.1 feet

So, the answers are

The x-coordinate of the vertex is 1.5

The maximum height of the ball occurs 1.5 feet from where it was thrown and the maximum height is 8.1 feet