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Compute Hockey Table Dimension Calculator

Hockey Table Dimension Calculator - Application of Quadratic Equation

Problem to solve:

The surface area of an air hockey table has an area of 60 square feet and a perimeter of 32 feet. What are the dimensions of the air hockey table?

Memory recall definition of area. Area of rectangular table is A = L x W and Perimeter of rectangular table is 2L + 2 W.

Condition 1 or Equation 1 to satisfy is the area,
A = L x W =

Do algebraic manipulation L = /w then substitute the value of L in equation 2 shown below.

Condition 2 or Equation 2 to satisfy is the perimeter,
P = 2L + 2W =

2 x ( / W ) + 2 w =

Do algebraic manipulation

You should get the new quadratic equation

w ² + w + = 0

w₁ = Width 1 answer

w₂ = Width 2 answer

L₁ = Length 1 answer

L₂ = Length 2 answer

How do you know if the answer is correct? Substitute the value of W1 and L1 both in equation 1 and equation. You should expect the answer are equal to 60 in equation 1 and 32 in equation 2.

If the answer is NaN (Not a Number). It means the answer is imaginary number .

Equivalent Quadratic Solution

Solution To Any Polynomial Equation

Factoring Any Polynomial Equation

The initial pattern for solving this type of problem is remembering the formula. Next mastering how to use your personal online calculator. Now you have your tool for computational thinking. You can do quick analysis. For example you can adjust 2 to 8, 1 to -1 and -6 to -11 .

Tip do not enter comma symbol because you will get an error message of NaN, meaning Not a Number data entry.

( X + ) ( X + ) = 0 ANSWER : FACTORS OF EQUATION

First root: X₁ = If answer is NaN, it means the answer is imaginary number.

X₁ = b + i The answer is imaginary number.

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Second root: X₂ = If answer is NaN, it means the answer is imaginary number.

X₂ = b - i The answer is imaginary number.

X₁ = ( b + Square Root ( b² - 4 a * c ) ) / 2 * a

X₁ = ( b + Square Root ( ) ) / =

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X₂ = ( b - Square Root ( b² - 4 a * c ) ) / 2 * a

X₂ = ( b - Square Root ( ) ) / =

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APPLICATION OF LESSON LEARNED:

Example (X + 2)(X - 1.5) = 0 is equivalent to quadratic equation x² + 0.5 x - 3 = 0

(X + 2)(X - 1.5) = 0 means when the value of y is set to zero (0) you can solve the value of x as shown by the graph below. (X + 2)(X - 1.5) = y(0)
y(0) is interpreted as , you set the value of y equal to zero then solve for the value x. Then you will get a pair coordinates (-2, 0 ) and (1.5, 0 )

y(1) is interpreted as, you set the value of x equal to 1 then solve for the value y. The answer is y(1) = -1.5 . Now you will have a new coordinate point (1, -1.5) and (-1, -1.5).

y(x) can be interpreted as the generalized quadratic equation or parabolic equation meaning you can assigned any real number value for x-coordinate and you can predict or expect a corresponding y-coordinate value.

y(x) is sometimes written as f(x) meaning the output value f(x) is a function of any input value of x. The lesson you learned about x-coordinate and y-coordinate is very important concept that you needed in real work application like Pi display dashboard, computer animation and factory automation.

Below is the solution using graphing method

Graph created using GeoGebra

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Click the link to solve using Wolfram Alpha

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