Given find the following a) Vertex b) Axis of Symmetry c) Y-intercept Warm Up 1) Convert from standard form to vertex form. y = x2 + 2x + 5 Given find the following a) Vertex b) Axis of Symmetry c) Y-intercept d) X-intercept
HW Check – 5.3 1) y = (x – 0)2 - 5 or y = x2 – 5 3) y = (x – 2)2 7) 19) y = (x + 2)2 – 4 20) y = 2(x + 2) 2 – 5 y = (x + 3.5) 2 – 11.25 31) Vertex (2, -4) y-int (0, 8) 33) Vertex (1, -1) y-int (0, 1)
Word Problems A ball is thrown in the air. The path of the ball is represented by the equation h = -t2 + 8t. What is the maximum height the ball reaches? How long does it take for the ball to hit the ground?
Word Problems A lighting fixture manufacturer has daily production costs of C = .25n2 – 10n + 800, where C is the total daily cost in dollars and n is the number of light fixture produced. How many fixtures should be produced to yield minimum cost.
Section 5.4 Factoring
GCF One way to factor an expression is to factor out a GCF or a GREATEST COMMON FACTOR. EX: 4x2 + 20x – 12 EX: 9n2 – 24n
Factors Factors are numbers or expressions that you multiply to get another number or expression. Ex. 3 and 4 are factors of 12 because 3x4 = 12
What are the following expressions factors of? 4 and 5 ? 5 and (x + 10) ? 3. (x + 3) and (x - 4) ?
Try Some! Factor: 9x2 +3x – 18 7p2 + 21 4w2 + 2w
Factors of Quadratic Expressions When you multiply 2 binomials: (x + a)(x + b) = x2 + (a +b)x + (ab) This only works when the coefficient for x2 is 1.
Finding Factors of Quadratic Expressions When a = 1: x2 + bx + c Step 1. Determine the signs of the factors Step 2. Find 2 numbers that’s product is c, and who’s sum is b.
Sign + + - + + - - - Factors (x + _) (x - _) (x - _) ADD SUBTRACT Sign table! Sign + + - + + - - - Factors (x + _) (x - _) (x - _) ADD SUBTRACT
Examples Factor: 1. X2 + 5x + 6 2. x2 – 10x + 25 3. x2 – 6x – 16 4. x2 + 4x – 45
Examples Factor: 1. X2 + 6x + 9 2. x2 – 13x + 42 3. x2 – 5x – 66 4. x2 – 16
Slide Factor Divide Reduce More Factoring! When a does NOT equal 1. Steps Slide Factor Divide Reduce
Example! Factor: 1. 3x2 – 16x + 5
Example! Factor: 2. 2x2 + 11x + 12
Example! Factor: 3. 2x2 + 7x – 9
Try Some! Factor 1. 5t2 + 28t + 32 2. 2m2 – 11m + 15
Teach Me How to Factor - Video
Homework – 5.4 & Unit 5A Test – Wed!!