FFPC+Mathematical+Reflections,+p+40

Abhishek 02/02/09 Big Understanding: Essential Question: Notes: No notes taken

1. **The quadratic expression x(x+7) is in factored form. How can you find an equivalent expression in expanded form? Write the expanded form for the expression, and sketch a rectangle to show that the two expressions are equivalent.**

We can find an equivalent expression in expanded form by sketching a rectangle out of the factored form expression and writing down the expressions of areas in terms of the original square for all the new rectangles to the original square. The expanded form is x^2+ x+ 7= x^2+7x

2. **The quadratic expression x^2+ 7x + 12 is in expanded form. How can you find an equivalent expression in factored form? Write the factored form for the expression, and sketch a rectangle to show that the two expressions are equivalent.**

We can find an equivalent expression in the factored form by finding which two numbers add up to 7 and if multiplied together, will give us a product of 12. These numbers are going to be the areas of two new rectangles, so the expressions are going to be something like (x+ one of the numbers) times (x+ the other number). The factored form of this expression is going to be (x+3) (x+4).

3. **In the graphs you made of the areas of the rectangles in this investigation, what information did the x-intercepts give you? How can you predict the x-intercepts for a quadratic function by looking at its equation?**

The x-intercepts gave us the information about where exactly does the graph touch the y-axis when X = 0. You can predict the x-intercepts for a quadratic functions from its equation by seeing if the equation has a part where x gets added or subtracted by a number or if a number gets + or – by x, the x-intercept is 0. If the equation has both x changing by a number, you multiply both numbers together.


 * 4. How can you recognize a quadratic function from its equation?**

Ans. We can recognize a quadratic function from its equation by seeing if the equation has X^2 part in it or if it has a (x + a number) for one dimension change and (x + a number) times (x + a number) for two dimension change.


 * 5. Describe what you know about the shape of the graph of a quadratic function. Include the line of symmetry and any other important features you have observed.**

The shape of the graph of a quadratic function is basically a parabola which is symmetrical if you draw a line of symmetry through the highest point in the graph if it is an upside down parabola, which is also called the maxim um point, or at the lowest point in a U-shaped parabola. This point is called the minimum point. The x-intercept is where the graph touches y-axis when X = 0 and y – intercept is where the graph touches x-axis when Y = 0.


 * Think about your answers to these questions, discuss your ideas with other students and your teacher, and then write a summary of your findings in your journal.**

Summary: In this investigation, we learned how to write expressions of quadratic functions. We also learned how to use equivalent expressions for the areas of rectangle with one dimension change and two dimensions change. We also learned how to write expressions in factored form and expanded form and we learned about like terms. We also learned about the different parts of parabolas which include the line of symmetry, x-intercept, y-intercept, maximum point and the minimum point.