Algebra 2B Big Ideas 8A
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This is a step by step guide for Big Ideas 8A.
Task #1A
This first task asks you to "Express the area A as a function of length L. Then write a list of everything you know about this function."
You learned in elementary school that Area = L x W. But for this question you want area in terms of only length. This means you need to know what the width is in terms of length. Then you can replace the width with its equivalent expression.
(Step #1)
So you need to find:
W = "expression which contains only L" (***See below if you're stuck finding the expression.)
(Step #2)
Then you can replace W with this expression in the Area formula:
Area = L x "expression which contains only L"
(Step #3)
Now that you have an formula for area in terms of only L, write everything that yo know about the function. Then you'll be done with Task #1A. Some ideas for you:
Task #1A
This first task asks you to "Express the area A as a function of length L. Then write a list of everything you know about this function."
You learned in elementary school that Area = L x W. But for this question you want area in terms of only length. This means you need to know what the width is in terms of length. Then you can replace the width with its equivalent expression.
(Step #1)
So you need to find:
W = "expression which contains only L" (***See below if you're stuck finding the expression.)
(Step #2)
Then you can replace W with this expression in the Area formula:
Area = L x "expression which contains only L"
(Step #3)
Now that you have an formula for area in terms of only L, write everything that yo know about the function. Then you'll be done with Task #1A. Some ideas for you:
- The Area function should be a quadratic function where the parabola opens downwards.
- The vertex point is the maximum point.
- You need to write the correct function.
- You should identify the (x, y) = (length, area) coordinates of the vertex.
- You should also identify the (x, y) = (length, area) coordinates of the two roots/zeros/x-intercepts of the parabola.
Task #1B
(This will be filled in later.)
(This will be filled in later.)
How to Find an Expression for W That Contains Only L
So you're trying to figure out how to find this expression that you need in Task #1A:
W = "expression which contains only L"
What specific information do you have about the rectangle? You know that "Rectangle R has varying length L and width W but with a constant perimeter 4 feet."
(Step #1)
Using this expression you can write an equation for perimeter:
P = "expression for perimeter containing both L and W"
(Step #2)
Go ahead and replace P with the 4 feet, since the you know that this is the rectangle's perimeter.
4 = "expression for perimeter containing both L and W"
(Step #3)
Now solve this equation for width in terms of length and you get this, which is what you needed in Task #1A.
W = "expression which contains only L"
W = "expression which contains only L"
What specific information do you have about the rectangle? You know that "Rectangle R has varying length L and width W but with a constant perimeter 4 feet."
(Step #1)
Using this expression you can write an equation for perimeter:
P = "expression for perimeter containing both L and W"
(Step #2)
Go ahead and replace P with the 4 feet, since the you know that this is the rectangle's perimeter.
4 = "expression for perimeter containing both L and W"
(Step #3)
Now solve this equation for width in terms of length and you get this, which is what you needed in Task #1A.
W = "expression which contains only L"