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Quadratic Equation Word Problem To Expression (Standard Form) - Area and Border

Level 1

The topics in this unit focus on constructing and solving quadratic equations from word problems. Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Quadratic Equation Word Problem To Expression (Standard Form) - Area and Border Worksheet

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Quadratic Equation Word Problem To Expression (Standard Form) - Area ...
1
A 5 by 9 painting has a border of width x on all sides. Its total area (border included) is 1.
What quadratic equation, in standard form, comes from calculating the area of the painting?
a A LaTex expression showing A(x) = 4x to the power of 2 + 28x + 49
b A LaTex expression showing A(x) = 4x to the power of 2 + 28x + 44
c A LaTex expression showing A(x) = -1x to the power of 2 + 26x + 44
2
A 11 by 6 painting has a border of width x on all sides. Its total area (border included) is 1.
What quadratic equation, in standard form, comes from calculating the area of the painting?
a A LaTex expression showing A(x) = 6x to the power of 2 + 38x + 65
b A LaTex expression showing A(x) = 4x to the power of 2 + 34x + 65
c A LaTex expression showing A(x) = 0x to the power of 2 + 34x + 65
3
A 4 by 8 garden has a ditch of width x on all sides. Its total area, including the ditch is 1.
What quadratic equation, in standard form, comes from calculating the area of the garden?
a A LaTex expression showing A(x) = 4x to the power of 2 + 24x + 31
b A LaTex expression showing A(x) = 2x to the power of 2 + 23x + 31
c A LaTex expression showing A(x) = 8x to the power of 2 + 24x + 31
4
A 4 by 2 painting has a border of width x on all sides. Its total area (border included) is 1.
What quadratic equation, in standard form, comes from calculating the area of the painting?
a A LaTex expression showing A(x) = 4x to the power of 2 + 12x + 12
b A LaTex expression showing A(x) = 4x to the power of 2 + 12x + 7
c A LaTex expression showing A(x) = 4x to the power of 2 + 13x + 7
5
A 9 by 11 painting has a border of width x on all sides. Its total area (border included) is 1.
What quadratic equation, in standard form, comes from calculating the area of the painting?
a A LaTex expression showing A(x) = 4x to the power of 2 + 40x + 98
b A LaTex expression showing A(x) = 3x to the power of 2 + 45x + 98
c A LaTex expression showing A(x) = 2x to the power of 2 + 40x + 100
6
A 7 by 6 painting has a border of width x on all sides. Its total area (border included) is 1.
What quadratic equation, in standard form, comes from calculating the area of the painting?
a A LaTex expression showing A(x) = 4x to the power of 2 + 28x + 45
b A LaTex expression showing A(x) = 3x to the power of 2 + 26x + 43
c A LaTex expression showing A(x) = 4x to the power of 2 + 26x + 41
7
A 9 by 4 garden has a ditch of width x on all sides. Its total area, including the ditch is 1.
What quadratic equation, in standard form, comes from calculating the area of the garden?
a A LaTex expression showing A(x) = 7x to the power of 2 + 30x + 35
b A LaTex expression showing A(x) = 4x to the power of 2 + 26x + 35
c A LaTex expression showing A(x) = 4x to the power of 2 + 31x + 38
8
A 3 by 11 painting has a border of width x on all sides. Its total area (border included) is 1.
What quadratic equation, in standard form, comes from calculating the area of the painting?
a A LaTex expression showing A(x) = 7x to the power of 2 + 28x + 28
b A LaTex expression showing A(x) = 4x to the power of 2 + 28x + 32
c A LaTex expression showing A(x) = 4x to the power of 2 + 33x + 27