Chapter 6 Linear L x ax b what happens if b 0 b 0 b 0 a 0 a 0 1 a 1 a 0 a 0 a is undefined Quadratic Q x ax2 bx c what happens if c 0 c 0 c 0 a 0 a 0 1 a 1 a 0 a 0 a is undefined 1 Positive Negative Horizontal Vertical Slope Intercept Standard Horizontal Vertical y mx b Ax By C y b x a This brings us back to the concept a linear equation has a degree of 1 identify The Equation Form Direction Slope y intercept x intercept Parallel Slope Perpendicular Slope 1 Slope intercept 2 Falling 3 3 4 7 5 7 3 7 3 6 3 7 7 2 L x 4x 7 if you need to find the zeroes x intercept solve for 0 etc Change the format L x 4 x 7 4 x would have to equal 7 4 for L x 0 L x ax b Q x ax2 bx c what happens if c 0 c 0 c 0 a 0 a 0 1 a 1 a 0 a 0 a is undefined what happens if b 0 b 0 b 0 a 0 a 0 1 a 1 a 0 a 0 a is undefined Q x ax2 bx c Factored form Q x a x p x q where p q Now what happens Note Page 99 Interval notation 3 p x p p q x q q Note Page 99 Interval notation p x p p q x q q Q x 0 Q x 0 Note Page 99 Interval notation p x p p q x q q Q x 0 pos Q x 0 Q x 0 neg Q x 0 Q x 0 pos Note Page 99 Interval notation 4 Positive Negative Zero at p p x p p q x q q Positive Zero at q Q x 0 pos Q x 0 Q x 0 neg Q x 0 Q x 0 pos Note Page 99 Interval notation Make some connections with prior knowledge 0 121 3 5 The degree is 2 y x2 y ax2 bx c y a x h 2 k y a x p x q y x2 y ax2 bx c y a x h 2 k y a x p x q the basic Standard Form Vertex Form Intercept Form Given any one of the equations you should be able to convert it into another form except for maybe the basic 4 vertex 0 0 line of symmetry x 0 x2 0 1 1 2 2 3 3 1 y 0 1 1 4 4 9 9 6 12 2 c y intercept b 2a x coordinate of the vertex use substitution to find the y coordinate x b 2a is the line of symmetry Now you can graph it 5 12 21 The yintercept is 2 5 12 21 The yintercept is 2 10 2 8 5 8 7 5 12 21 The y intercept is 2 10 2 8 5 8 y 8 5 8 2 10 5 8 2 1 125 or 9 8 Vertex 5 8 9 8 5 12 21 The y intercept is 2 10 2 8 5 8 y 8 5 8 2 10 5 8 2 1 125 or 9 8 Vertex 5 8 9 8 so with the line of symmetry we can find the third point 5 8 5 8 2 10 8 2 5 12 21 Connect the plotted points 8 6 5 12 21 y 8x 2 x 1 y 2 4x 1 x 1 This is the intercept form Equate the quantities to 0 to find the intercepts 4x 1 0 or x 1 0 x 1 4 or x 1 as shown in the graph 6 p q a x intercepts opens up down wide skinny can expand to find the vertex and line of symmetry 7 8 9 What does a denote What does c denote How do these coefficients effect the graph 9 the quadratic formula will work every time x b b 2 4ac 2a This should be familiar now match it to the text 0 x b b 2 4ac 2a b b 2 4ac x 2a 2a x b b 2 4ac 2a b b 2 4ac x 2a 2a 10 x b b 2 4ac 2a b b 2 4ac x 2a 2a b b 2 4ac x 2a 2a u x b 2a m b 2 4ac 2a b b 2 4ac x 2a 2a b u x 2a b 2 4ac m 2a M b 2 4ac 4a 2 to see proof go to section 1 5 11 Q x a u2 M b u x 2a 4 b u x 2a if M 0 if a 0 if a 0 4 b 2 4ac M 4a 2 b 2 4ac M 4a 2 No real roots Minimum Maximum b u x 2a b 2 4ac M 4a 2 if M 0 or a double root same idea regarding max min if a 0 if a 0 Minimum Maximum 12 4 b u x 2a b 2 4ac M 4a 2 if M 0 or 2 real roots u b 2 4ac 2a A B Find your vertex b 2a How do you know if it will be a maximum or a minimum Identify the intervals Q x negative Q x positive 13