Math Reflection 2

1. The side lengths of a rectangle might be x+4, and x+6. To find out the total area, you would multiply each value by eachother. You could use to equation (x+4)(x+6). It would come out to x^2 + 4x + 6x + 24, or x^2 + 10x + 24.

2a. You can use the Distributive Property to change a quadratic expression from its factored form into its expanded form. A quadratic expression in factored form can look like (x+3)(x+5). To change it to its expanded form, you each value to the three others, getting four new values. In this case, they would be x^2 + 3x + 5x + 15, or x^2 + 8x + 15.

2b. You can use the Distributive Property to change a quadratic expression from its expanded form into its factores form. A quadratic expression in its expanded form could look like x^2 + 8x + 12. To change it, you have to find out what two numbers, when added, add up to 8, and when multiplied, come out to 12. The two numbers are 2 and 6. When you find these out, the equation will look like (x+2)(x+6).

3. It is very easy to recognize a quadratic function from its equation. All quadratic expressions have an x^2 somewhere in their expanded form. You may mix them up with exponential expressions, so you have to remember, in exponential expressions, the variable is the exponent. In quadratic expressions, the variable is the base.

4. The graphs of quadratic functions are called parabolas. They open either up or down, are symmetrical, and have a vertex. They all have a y-intercept, and have either 2, 1, or 0 x-intercepts. In a quadratic equation, x^2 represents the slope. 2x^2 is steeper than x^2, while 1/3x^2 is less steep. The next part,(in the expanded form), for example, 8x, would represent the two x-intercepts added together. It is much easier to tell what they are in factored form. So, if the equation was (x+4)(x+4), the one x-intercept would be (-4, 0). In this case, the x-intercept is the vertex. The last part(in the equations expanded form), would be 16. This is the y-intercept. For this equation, the y-intercept would be 16.