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Chapters 1 & 2 Review Day
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Test Topics Chapter 1 Find a linear equation from two points.
Find a linear equation from a point and a parallel or perpendicular line. Solve a systems of equations. Write and evaluate an equation from a linear model. Solve a quadratic by factoring. Solve a quadratic by quadratic formula.
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Test Topics Chapter 2 Divide a polynomial.
Sketch the graph of a polynomial. Write a possible equation from a graph of a polynomial. Find zeros of a polynomial on the calculator. Find min/max of a polynomial on the calculator. Write a quadratic function from a situation, find the domain & the min or max. Write a cubic function from a situation, find the domain & the local min or max. Solve a polynomial by grouping terms or rewriting in quadratic form. Find a quadratic equation given the roots.
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Make a sketch and write an equation for each situation:
1. A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement? 2. A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway? 3. You have to make a square-bottomed, unlidded box with a height of three inches and a volume of approximately 42 cubic inches. You will be taking a piece of cardboard, cutting three-inch squares from each corner, scoring between the corners, and folding up the edges. What should be the dimensions of the cardboard, to the nearest quarter inch?
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1. Let "w" stand for the width of the picture.
The height h is 4/3 the width, so h = (4/3)w. Then the area is A = hw = [(4/3)w][w] = (4/3)w2 = 192. I need to solve this "area" equation for the value of the width, and then back-solve to find the value of the height. (4/3)w2 = 192 w2 = 144 w = ± 12
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