THE BOWLING QUESTION Jude’s Drafting Table Bowling alley by flickr user strollerdos Retro Bowl by flickr user FotoEdge

THE QUESTION: The arrangement of the ten bowling pins formed a parabola. The division between the carpet and the wooden floor forms the x-axis. The pins were placed in four rows where the number of pins in each row was equal to the number of the row. The central and only pin in the first row acted as the vertex that lied directly on the y-axis.

THE QUESTION:

The arrangement of the ten bowling pins formed a parabola. The division between the carpet and the wooden floor forms the x-axis. The pins were placed in four rows where the number of pins in each row was equal to the number of the row. The central and only pin in the first row acted as the vertex that lied directly on the y-axis.

THE QUESTION: The distance from the vertex to a focus point in the fourth row was 4. The focus point on the fourth row was situated at (0, 8). Lucy handed me paper and demanded an equation and the sketch of the graph. She found that the question was too easy so she told me to justify whether or not the parabola passed through the point (4, 5).

The distance from the vertex to a focus point in the fourth row was 4. The focus point on the fourth row was situated at (0, 8). Lucy handed me paper and demanded an equation and the sketch of the graph. She found that the question was too easy so she told me to justify whether or not the parabola passed through the point (4, 5).

.:. THE DIAGRAM .:. CARPET WOODEN FLOOR FOCUS POINT (0, 8) VERTEX (h, k) parabola y x p = 4

.:.WHAT WE KNOW .:. formation of the bowling pins forms parabola. division between carpet and wooden floor is the x-axis. central pin  vertex  (h, k) and lies on y-axis. Row I = 1 pin, Row II = 2 pins, etc… up to 4 rows. p = 4 , therefore 1 pin = 1 unit since there are four rows focus point = (0, 8) general formula of parabola : [vertical does not apply] HORIZONTAL  (x – h) 2 = 4p (y – k) coordinate given = (4, 5)

formation of the bowling pins forms parabola.

division between carpet and wooden floor is the x-axis.

central pin  vertex  (h, k) and lies on y-axis.

Row I = 1 pin, Row II = 2 pins, etc… up to 4 rows.

p = 4 , therefore 1 pin = 1 unit since there are four rows

focus point = (0, 8)

general formula of parabola : [vertical does not apply]

HORIZONTAL  (x – h) 2 = 4p (y – k)

coordinate given = (4, 5)

THE SOLUTION…

STEPS PROCESS After analyzing the given information, we must remember the standard formula of a parabola which is: (x – h ) 2 = 4 p (y – k ). Then plug in the numbers from the coordinates given in the question; p = 4 , and the vertex is (0, k). The vertex is still unknown but it could be found by using the focus point and p . *reminder: p is the distance from the focus point to the vertex. We know h = 0 since it lies on the y-axis. In order to get k, subtract p from the y-coordinate from the focus point. Finally, plug in the values to find the equation.

STEPS

PROCESS

After analyzing the given information, we must remember the standard formula of a parabola which is: (x – h ) 2 = 4 p (y – k ).

Then plug in the numbers from the coordinates given in the question; p = 4 , and the vertex is (0, k).

The vertex is still unknown but it could be found by using the focus point and p . *reminder: p is the distance from the focus point to the vertex.

We know h = 0 since it lies on the y-axis. In order to get k, subtract p from the y-coordinate from the focus point.

Finally, plug in the values to find the equation.

(6) As for the second part of the question, to find out if (4, 5) was a point on the parabola, recall that they are points on a graph, (x, y). Plug those numbers in the formula. If the values are equal to each other, the point lies on the parabola. STEPS PROCESS

(6) As for the second part of the question, to find out if (4, 5) was a point on the parabola, recall that they are points on a graph, (x, y). Plug those numbers in the formula. If the values are equal to each other, the point lies on the parabola.

STEPS

PROCESS

.:. THE GRAPH .:.

QUESTION COMPLETE… Now that this is out of the way, there’s nothing much that will stop me from loving Lucy… evan rachel wood by flickr user sarah grutas

Now that this is out of the way, there’s nothing much that will stop me from loving Lucy…