Math Reflection 2

1. The area of a rectangle can illustrate the Distributive Property. For example, if the rectangle is split into four parts, the sides of the original square would both be x and the two additional sides might be 2 and 4. You multiply all the values to each other to find the area of each of the four sections. One would be x^2, one would be 2x, one would be 4x, and the fourth would be 8. You combine the four areas and the equation would be x^2+8x+8.

2a. If a quadratic expression is in factored form, you can change it to expanded form using the Distributive Property. If the equation was (x+3)(x+4), you multiply each term by the other three: x(x), x(3), x(4), 3(4). You get x^2+3x+4x+12, and you combine like terms to get the final equation: x^2+7x+12.

b. If a qaudratic expression is in expanded form, you can change it to factored form using the Distributive Property. If the equation was x^2+11x+30, you have to break up all the terms. x^2 becomes x and x. To figure out the other two terms, you have to find a pair of values that add up to 11 and multiply together to 30. The pair is 5 and 6 because 5+6=11 and 5(6)=30. The new equation is (x+5)(x+6).

3. You can recognize a quadratic function from its equation if it has an exponent that's not a variable (expanded form) or if it has two quantities containing x that are being multiplied (factored form).

4. The graph of a quadratic function is a parabola. The x-intercepts are the opposite of the two numbers in the equation. If the equation is (x+9)(x-2) the x-intercepts are -9 and 2. The y-intercept is the last term in the expanded form equation. If the equation is x^2+5x+6 the y-intercept is 6.