this equation represents the area of a rectangular chicken coop a=2x2-4x+2
To find the area of the rectangular chicken coop, we can use the equation: A = 2x^2 - 4x + 2.
The equation is in the form of a quadratic function, where A represents the area of the coop and x represents the length or width of the coop.
To simplify the equation and get the area, we can follow these steps:
Step 1: Start with the equation A = 2x^2 - 4x + 2.
Step 2: Since this is a quadratic equation, we need to determine its roots, which will help find the x-intercepts or the dimensions of the rectangular coop.
Step 3: To find the roots, set the equation equal to zero: 2x^2 - 4x + 2 = 0.
Step 4: Next, we can try factoring the quadratic equation. However, this equation cannot be factored easily. In such cases, we can use the quadratic formula, which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions or roots can be found using the formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a.
In our case, a = 2, b = -4, and c = 2. Plugging these values into the formula, we get: x = (-(-4) ± sqrt((-4)^2 - 4(2)(2))) / (2(2)). Simplifying this further, we have: x = (4 ± sqrt(16 - 16)) / 4. This simplifies to: x = (4 ± sqrt(0)) / 4 = (4 ± 0) / 4 = 1.
Step 5: We found that the roots or x-intercepts of the equation are both equal to 1, which means the dimensions of the rectangular chicken coop are 1 unit by 1 unit.
Step 6: Now, we can substitute the value of x back into the original equation to find the area. Using x = 1, we have: A = 2(1)^2 - 4(1) + 2 = 2 - 4 + 2 = 0.
Therefore, the area of the rectangular chicken coop is 0 square units.