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Transcript
Please Focus as we review to prepare ourselves for quadratic equations! Solving Equations ► “It’s impossible to solve a single equation with two variables and get a single solution.” ► “For example, for the equation” 3x + 2y = 100 if x=0 y=50, if x=5 y=85, if x=10 y=35……. ► We solved equations like this by making a chart and choosing any number for x and solving for y. Solving Equations (continued) ► We also solved these by putting them in slope-intercept form and graphing them. Standard form- Ax + By = C 3x + 2y = 100 Slope intercept formy = mx +b m=slope, b=y intercept y = -3/2 x + 50 Classifying equations with 2 variables. On your paper make a t-chart with 2 columns: Standard form/ Slope intercept Put the following equations in the correct column. 1. 3x + 2y = 17 2. 7/2x – 4y = -20 3. y = 1/2 x + 6 4. x + y = 4 5. y = -2x – 8 6. y=5 ► Standard Form 3x + 2y = 17 7/2x – 4y = -20 x+y=4 y intercept form y = 1/2 x + 6 y = -2x – 8 y=5 Now for each problem write A= B= C= m= b= Linear Systems For some problems, two equations were needed. If you have two equations with two variables each, only one value of x and one value of y will make both equations true. For example- in Standard form3x - 2y = 5 3x + 2y = 13 x=3 y=2 Linear Systems (continued) What three ways did we use to solve linear systems? Substitution Elimination Graphing Linear Systems (continued) What three ways did we use to solve linear systems? Substitution – put y by itself in one equation and substitute it into the other and solve for x Elimination- addition, subtraction, multiplication Graphing- put both equations in slope intercept form. Where the two lines interceptThat’s the solution!!!!! Quadratic Equations “A quadratic equation is an equation with a variable to the second power but no variable higher than the second power.” “A quadratic equation has the form ax2 + bx + c = 0 where a is not equal to zero” Quadratic Equations “Examples – A. X2 + 3x + 5 = 0 B. 3x2 - 4x + 3 = 0 C. -5x2 - 2x = 7 D. X2 + 3x = 0 E. X2 – 36 =0 For each of these examples please writea= b= c= Quadratic Equations For the following equations write “yes” if it is a quadratic equation and “no” if not. A. B. C. D. E. x2 + 4x -9 = 0 x2 – 4x - 6 X3 – 4x2 + 6 =0 2x - 6 = 0 -3x2 -45 =0 Quadratic Equations Q E can be solved in three main ways– – – Graphing Factoring Quadratic Formula Quadratic Equations The quadratic formula is