On this week, we reviewed chapter 1, 2, 3, 4 and we learned new chapter, Graphing Inequalities and systems of Equations. At chapter 1, we learned arithmetic sequences, arithmetic series, geometric sequences, and geometric series. At chapter 2 , we learned absolute value and about radicals. At chapter 3, we learned solving quadratic equations. At chapter 4, we learned analyzing quadratic functions. The specific details about chapter 1, 2, 3, 4 are on my previous blog post. Also on this week, we took the midterm test on Wednesday. And we started new chapter, this chapter is about graphing inequalities and systems of equations. In section 5.1, we learned solving quadratic inequalities in one variable. The general form are 
+ bx+ c < 0, +bx +c > 0 , +bx + c ≥ 0, and +bx +c ≤ 0. The x-intercept of the graph of a quadratic function are called the critical values of the corresponding quadratic inequality. These values can be used to illustrate the solution of the inequality on a number line. For example, the solution of 
+5x -6 < 0. At first you have to factor. If you factor this example, it will be (x+6)(x-1) < 0. And if you illustrate the number line, you can find the solution. The solution is -6 < x < 1.
Ex) Solve each quadratic inequality.
– 16x + 12 > 0. At first, you have to fine common factor. The common factor is 4. To divide by 4. Then the equation will be – 4x + 3 > 0 and then to factor. (x-3)(x-1) > 0 and to draw the number line, then the solution is 1 < x < 3.
Ex) A tennis ball is thrown upward at an initial speed of 24m/s. The approximate height of the ball, h metres, after t seconds, is given by the equation h=24t- 
. Determine the time period for which the ball is higher than 20m.
(24t- > 20)* -1/4 if you multiply both sides by minus, you must change the direction of the inequality sign. $latex t^2 -6t +5 < 0 and then to change factored form. (t-5)(t-1) < 0 and draw the number line and find the time period for which the ball is higher than 20m.
this is how to solve my self made question.
