4.4+Solving+Quadratic+Equations+0910


 * 5-4-10**
 * JO** **(Jee Hoon Oh)**
 * Big Idea:** Equations can be used to model real things.
 * Essential Question:** How do I create and solve equations?
 * Notes From Class:** Finding the x intercept of y=x^2+5x is same as solving the equation x^2+5x=0. The solutions to x^2+5x=0 are called the roots of the equation y=x^2+5x. If R is the root of a equation, then the point (r,0) is the x-intercept of the graph.

=__**4.4**__=


 * A. The Expression x^2+3x is in expanded form. Write an equivalent expression in factored form**.

X(x+3)


 * B. Find all possible solutions to the equation X^2+3x=0. Explain how you know you have found all the solutions.**

If you substitute 0 with x, then the equation would equal 0. 0^2+3 x 0= 0 0+0= 0

Also if you substitute x with -3 it would also equal 0 -3^2+3 x -3 = 0 9-9 = 0


 * C. What are the x-intercepts of y=x^2+3x? Explain how your answers to part B can help you answer this question**

As we know from Problem B that Y=0, we found out that x is 0 and -3. And therefore the x intercepts are 0 and -3


 * D. Which form of the expression X^2 + 3x, the expanded form or the factored form, is more useful for finding the roots, or x-intercepts, of the equation y=X^2+3x? Explain your reasoning**

The expanded form of the expression X^2+3x is more useful for finding the roots because the expanded form shows you the actual value of the x while for the factored form, you have to multiply to get the actual value of x.


 * E. In 1 and 2, an equation is given for both the factored form and the expanded form of a quadratic expression. Find the roots, or x-intercepts, of the equation without making a table or a graph, and tell which form of the equation you used to find your answer.**

The x intercept is 0 and 2. I used the expanded form of the equation.
 * 1. y=4x^2-8x or y=4x(x-2)**


 * 2. y=6x(5-2x) or y=30x-12x^2**


 * F. In 1-3, solve the equation by first factoring the quadratic expression.**

(x+4.5)+(x+0)
 * 1. x^2+4.5x=0**

x+9)+(x-0) =0
 * 2. x^2-9x=0**

(x+10)+(x-0) =0
 * 3. -x^2+10x=0**

=__**F.U**__=

I can substitute x with 0 for all of them and it will equal 0 which means its correct.
 * 1. Check your answers to part F without using a table or a graph.**

0^2+4.5 x 0= 0

0^2-9 x 0= 0

-0^2+10 x 0= 0


 * 2. Check your answers to part F by making graphs and finding the x-intercepts.**

1. x intercepts= 0, -4.5

2. x intercepts- 0, -9

3. x intercepts- 0, -10


 * 3. a. For each expression below, find an equivalent expression in expanded form.**

2x^2+10x+x+5
 * i. (2x+1)(x+5)**

x^2-2x+2x-4
 * ii. (x+2)(x-2)**


 * 3. b. Which form of the expression would you use to predict the x-intercepts of the related graph? Find the x-intercepts and explain your reasoning.**

I would use the expanded form because like i said before the expanded form already shows the exact x values while for the factored form you have to multiply in order to get to that stage.


 * 4. Use the diagram below to find the linear factors of x^2+8x+12. Use the factors to solve the equation x^2+8x+12=0**

The x intercept is -2.

-2^2+8 x -2+12=0 4+(-16)+12=0 -12+12=0