Math Reflection 2

1. The area of a rectangle can illustrate the distributive property. If the squares original length is "x" the equation would be x^2. Then if you wanted to add 7 to one side and 4 to the other the equation would be A=(x+7)(x+4), A being the area. Then you distribute to get the area:
A=(x+7)x+(x+7)4
A=x^2+7x+4x+28
A=x^2+11x+28

2.a. If a quadratic expression is in factored form and you want it in expanded form you do the following:
A=(x+9)(x+6)
A=(x+9)x+(x+9)6 Use the distributive property to multiply (x+9) by x and 6.
A=x^2+9x+6x+54 Distribute.
A=x^2+15x+54 Combine like terms. (you don't have to)

2.b. If a quadratic expression is in expanded form and you want it it factored form do the following:
A=x^2+7x+10
A=x^2+5x+2x+10 Find two numbers that add up to seven and multiply to 10.
A=(x+5)(x+2) Put into factored form.

3. You can recognize a quadratic function from it's equation because in a quadratic function's equation there is always and x^2 (for expanded form) or two X's being multiplied (for factored form).

4. Features of a quadratic function's graph are:
*Parabola(u shaped)

*Symmetrical-to find the equation for the line of symmetry is the number exactly between the two x-intercepts. The equation would be x=a.

*Has a maximum/minimum point-the x coordinate would be the number exactly in between the two x-intercepts and then you substitute the x in the equation to find the y coordinate.

*x-intercept(s)-these are the oposites of the two constants in the factored equation. If there is only one constant the other is 0.

*y-intercept-the constant or the number with no variable in the expanded equation.