Question

A golf player is trying to make a hole-in-one on the miniature golf green shown.

Imagine that a coordinate grid is placed over the golf green. The golf ball is at (2, 1.6) and the hole is at (7.6, 1.6). The player is going to bank the ball off the side wall of the green at (4.8, 6.4).

Part 1 out of 2
Enter an equation for the path of the ball. Enter the parameter a as a fraction in lowest terms.
y=

Answer 1

The path of the ball is an illustration of absolute equation.

The equation of the path is: $y =- \frac{12}7|x- 4.8| + 6.4$

The given parameters are:

$(h,k) = (4.8,6.4)$ --- the vertex (i.e. the point where the ball hits the wall)

$(x_1,y_1) = (2,1.6)$

$(x_2,y_2) = (7.6,1.6)$

An absolute function is represented as:

$y = a |x - h| + k$

Substitute $(h,k) = (4.8,6.4)$

$y = a |x - 4.8| + 6.4$

Substitute $(x_1,y_1) = (2,1.6)$ for x and y

$1.6 = a|2 - 4.8| + 6.4$

$1.6 = a|- 2.8| + 6.4$

Remove absolute bracket

$1.6 = 2.8a + 6.4$

Collect like terms

$2.8a = -6.4+1.6$

$2.8a =- 4.8$

Solve for a

$a =-\frac{4.8}{2.8}$

Simplify

$a =-\frac{12}{7}$

Substitute $a =-\frac{12}{7}$ in $y = a |x - 4.8| + 6.4$

$y =- \frac{12}7|x- 4.8| + 6.4$

Hence, the equation of the path is: $y =- \frac{12}7|x- 4.8| + 6.4$

See attachment for graph that models the path

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