4.4+Solving+Quadratic+Equations+0809

Sidratun 03.21.09 Saturday Block- 8D __4.4 Solving Quadratic Equations __ X(x+3) x=0 Substitute 0 for the value of x into the equation. 0.0+3.0=0 0+0=0 So, x^2+3x=0 X=-3 Substitute -3 for the value of x into the equation. -3.-3+3.-3=0 9+-9=0 0=0 As we already know form problem B that y=0, we found out that x is 0, -3. And therefore the x intercepts are o and -3. The expanded form of the expression x^2+3x is more useful for finding the roots, x intercepts of the equation y=x^2=3x. This is because the expanded form gives us information on the y intercept; they give us the value of y. 1. (x+-4.5) +(x-0) =0 2. (x+9)+(x-0) =0 3. (x+10)+(x-0) =0 F O L L O W – U P __** x || y || x || y || x || y || -5 || 2.5 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">-4.5 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; color: black; font-family: 'Times New Roman','serif'; mso-themecolor: text1;">1 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-8 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">2 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">11 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-4 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-2 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">2 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-14 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">3 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">24 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-3 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-4.5 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">3 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-18 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">4 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">39 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-2 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-5 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">4 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-20 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">5 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">56 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-1 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-3.5 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">5 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-20 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">6 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">75 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; color: black; font-family: 'Times New Roman','serif'; mso-themecolor: text1;">6 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-18 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">7 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">96 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">1 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">5.5 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">7 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-14 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">8 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">119 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">2 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">13 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">8 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">-8 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">9 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">171 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">3 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">22.5 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">9 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">-10 || <span style="font-size: 12pt; color: red; font-family: 'Times New Roman','serif';">0 || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';"> <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">1.x intercepts- 0, -4.5 <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">2. x intercepts- 0, -9 <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">3. x intercepts- 0, -10 <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">(**x+2)(x-2)** x^2+4x+4 <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">
 * <span style="font-size: 12pt; color: #7f7f7f; font-family: 'Times New Roman','serif'; mso-themecolor: text1; mso-themetint: 128;">NOTES- use y=0 to find the x intercept. **
 * <span style="font-size: 12pt; color: #7f7f7f; font-family: 'Times New Roman','serif'; mso-themecolor: text1; mso-themetint: 128;">The root of the expression x^2+6x+8 is -2 and -4. **
 * <span style="font-size: 12pt; color: #7f7f7f; font-family: 'Times New Roman','serif'; mso-themecolor: text1; mso-themetint: 128;">How do I know which shape a parabola is? **
 * <span style="font-size: 12pt; color: #7f7f7f; font-family: 'Times New Roman','serif'; mso-themecolor: text1; mso-themetint: 128;">If it is a u, it is positive. **
 * <span style="font-size: 12pt; color: #7f7f7f; font-family: 'Times New Roman','serif'; mso-themecolor: text1; mso-themetint: 128;">If it is an upside down u, it is a negative. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">A. The expression x^2+3X is in expanded form. Write an equivalent expression in factored form. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">B. Find all possible solutions to the equation x^2+3x=0. Explain how you know you have found all the solutions. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">C. what are the x-intercepts of y=x^2+3x. Explain how your answers to part b can help you answer this question. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">D. Which form of the expression x^2+3x, the expanded from or the factored form, is more useful for finding the roots, or x-intercepts, of the equation y=x@+3x? Explain your reasoning. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">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 graph, and tell which form of the equation you used to find your answer. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">1. Y=4x2-8x or y=4x(x-2) 2. Y=6x (5-2x) or y=30x-12x^2 **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">1. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">F. in 1-3, solve the equation by first factoring the quadratic expression. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">1. X^2+4.5x=0 2. X^2-9x=0 3.-x^2+10x=0 **
 * __<span style="font-size: 12pt; font-family: 'Times New Roman','serif';">
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> 1.  ****<span style="font-size: 12pt; font-family: 'Times New Roman','serif';">Check your answers to part f without using a table or a graph. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> 2.  ****<span style="font-size: 12pt; font-family: 'Times New Roman','serif';">Check your answers to part F by making graphs and finding the x-intercepts. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif'; mso-fareast-font-family: 'Times New Roman';"> 3.  ****<span style="font-size: 12pt; font-family: 'Times New Roman','serif';">A. For each expression below, find an equivalent expression in expanded form. **
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">(2x+1)(x+5) **<span style="font-size: 12pt; font-family: 'Times New Roman','serif';">2x^2+11x+5
 * <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">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. **