Question

Use the table to answer the question.

Table Showing Distance and Height of Golf Ball Path
Distance (yards) Height (yards)
0 0
56 26
112 34
168 26
224 0
The table represents the path of a golf ball as it is hit by a golf club. Using technology, create an equation to model the situation. In the equation, what is the value of a? Round to the nearest thousandth.

(1 point)
In the equation that models this situation,
a
=
.

Answer 1

To model the path of the golf ball based on the distances and heights given in the table, we can assume that the path follows a quadratic equation of the form:

\[ h(x) = ax^2 + bx + c \]

Where:
- \( h(x) \) is the height of the golf ball in yards.
- \( x \) is the distance in yards.
- \( a \), \( b \), and \( c \) are constants to be determined.

The table provides the following points:
1. \( (0, 0) \)
2. \( (56, 26) \)
3. \( (112, 34) \)
4. \( (168, 26) \)
5. \( (224, 0) \)

Since the golf ball starts and ends at height 0, we know that the quadratic will be of the form:

\[ h(x) = a(x)(x - 224) \]

This structure is chosen because we know the height is 0 at \( x = 0 \) and \( x = 224 \).

To find the value of \( a \), we can substitute one of the other points into the equation. Let's use the point \( (112, 34) \):

Substituting \( x = 112 \) and \( h(112) = 34 \):

\[ 34 = a(112)(112 - 224) \]
\[ 34 = a(112)(-112) \]
\[ 34 = -12544a \]

Now, solving for \( a \):

\[ a = \frac{34}{-12544} \]
\[ a \approx -0.00271 \]

Rounding to the nearest thousandth:

\[ a \approx -0.003 \]

Thus, the final answer is:

**In the equation that models this situation, a = -0.003.**