1. The area of a rectangle illustrates the Distributive Property because it allows you to see how the different parts of the side legnth affect the overall area. When you have an equation for the area of a rectangle, you often need to distribute to find another form or a value. For example, with the equation A=(x+3)(x+4), you would distribute the x to both the numbers in the second parenthesis, and then the 3, to get the expanded form of the equation.
2.a. If an equation is in factored form, you use the Distributive Property to find the equation in expanded form. For the equation y=(x+2)(x+4) you would distribute the numbers in the first set of parenthesis to both the numbers in the second parenthesis.
b. If an equation is in expanded form and you need to put it in factored form you can use an almost reverse distributive property. If the equation is y=x^2+7x+10, you first find two numbers that add up to 7 and multiply to 10, 5 and 2. You rewrite the equation as y=x^2+5x+2x+10. You then look at the numbers and find, for every set of two numbers, the thing in common. For this equation you have x in common for x^2 and 5x, so you write x(x+5) then you add to that what you get from the other two numbers. In common from 2x and 10, you get 2. So you write, 2(x+5). In both the parts you have something in common, (x+5). You take this as one of the sets in parenthesis, and for the other, you take the things that were multiplied into those parenthesis and get (x+2), so you have y= (x+5)(x+2).
3. You can recognize a quadratic function from its equation if it has the right form, either the expanded form or the factored form.
4. The graph of a quadratic function is a parabola, an symmetrical ark-shape. Some important features on these graphs are the x and y-axis, the minimum\maximum point, and the line of symmetry. You find the x-intercepts by finding the two numbers added to x in the factored form of the equation. You find the y-intercept by if there is a number added\subtracted in the expanded form. You can find the minimum\maximum point by adding together the x-intercepts and dividing by 2 to get the x coordinate. To find the y coordinate you plug the x coordinate into the equation and solve. The line of symmetry is the x-coordinate of the minimum\maximum point.
by Allie :)
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1 comment:
Hi Allie,
Your explanation helped me understand the information in a way I hadn't thought about it. The way that you explained part 2b was a little different than how I explained it and that was good because it made me look at it in two different ways which helped me understand it better. :)
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