To begin a football game, the kicker has to kick off. The football follows the path h(x) = −130x(x−60)

Let's analyze the function \( h(x) = -130x(x-60) \), which describes the height of the football as a function of the horizontal distance traveled, \( x \).

### 1) What is the y-intercept?

The y-intercept occurs when \( x = 0 \). To find the y-intercept, we will substitute \( x = 0 \) into the height function:

\[
h(0) = -130(0)(0-60) = -130(0)(-60) = 0
\]

Thus, the y-intercept is \( (0, 0) \).

### 2) At what time is the football at the highest height?

To find the highest point of the parabola represented by \( h(x) \), we can find the vertex. The function is a downward-opening parabola (since the coefficient of \( x^2 \) is negative).

The x-coordinate of the vertex (the maximum height) can be found using the formula:

\[
x = -\frac{b}{2a}
\]

In our case, we can rewrite \( h(x) \) as:

\[
h(x) = -130(x^2 - 60x)
\]

Here, \( a = -130 \) and \( b = 130 \) (as we can treat \( b \) as the coefficient of \( x \)). Therefore,

\[
x = -\frac{60}{2 \times -130} = \frac{60}{260} = \frac{3}{13}
\]

So, the football reaches its maximum height at \( x = \frac{3}{13} \) yards.

### 3) The ball will have traveled how many yards before hitting the ground?

The football will hit the ground when the height \( h(x) = 0 \). We set the height function equal to zero:

\[
-130x(x-60) = 0
\]

This gives us two factors:

1. \( -130x = 0 \) → \( x = 0 \)
2. \( x - 60 = 0 \) → \( x = 60 \)

So, the football will hit the ground after it has traveled \( 60 \) yards.

### Summary of Answers:
1) The y-intercept is \( (0, 0) \).
2) The football reaches its highest height at \( x = \frac{3}{13} \) yards.
3) The ball will have traveled \( 60 \) yards before hitting the ground.