Remember scientific notation?. (1.2 x 10 -3 )(6.7 x 10 6 ) Small # Big # 8.04 x 10 -3+6 8.04 x 10 3.

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Presentation transcript:

Remember scientific notation?

(1.2 x )(6.7 x 10 6 ) Small # Big # 8.04 x x 10 3

(8.2 x 10 8 )(6.7 x 10 6 ) or x x 10 1 x x 10 15

(8.2 x )(9.7 x ) or x x 10 1 x x 10 -6

Simplify. Answer must have positive exponents.

Sketch a graph. y = -2x x intercepts: y intercept: vertex: none (0,-4) Means: as x approaches negative infinity, so does y Remember y is f(x) END BEHAVIOR:

Sketch a graph. y = -x x intercepts: y intercept: vertex: (2,0)(-2,0) (0,4)

Sketch a graph. y = x x intercepts: y intercept: Domain: Range: (-1.26,0) (0,2) (-∞,∞)

Sketch a graph. y = (x-3) x intercepts: y intercept: vertex: none (0,11) (3,2)

Sketch a graph. y = x 4 x intercepts: y intercept: Domain: Range: (0,0) (-∞,∞) [0,∞) y = x 2

Sketch a graph. y = x 5 x intercepts: y intercept: Domain: Range: (0,0) (-∞,∞)

Sketch a graph. y = -x 4 –x 2 + x - 2 x intercepts: y intercept: Domain: none (0,-2) (-∞,∞)

What methods (tools) do we use to find x intercepts? FactoringQ.F. GCF (x+ )(x+ ) 6 step method grouping 2x x + 15 x 3 + 5x 2 – 9x - 45 x 2 - x x 2 - 6x 2x x + 15 x 3 + 5x 2 – 9x - 45 x 2 - x x 2 - 6x 2x x + 15 x 3 + 5x 2 – 9x - 45 x 2 - x x 2 - 6x 2x x + 15 x 3 + 5x 2 – 9x - 45 x 2 - x x 2 - 6x 2x x + 15 x 3 + 5x 2 – 9x - 45 x 2 - x x 2 - 6x

What methods (tools) do we use to find x intercepts? Factoring GCF (x+ )(x+ ) 6 step method grouping 3x 2 - 6x x 2 - x x x + 15 x 3 + 5x 2 – 9x - 45 difference of perfect squares 4x (2x – 7)(2x + 7)

Factoring a Cubic 8x Step 1: Take the cube root of each term. (2x + 3) Step 2: Square the first term. Multiply the two terms together and change the sign. Square the last term (2x + 3)(4x 2 -6x+9)

Factoring a Cubic 27x Step 1: Take the cube root of each term. (3x - 4) Step 2: Square the first term. Multiply the two terms together and change the sign. Square the last term (3x -4 )(9x 2 +12x+16)

Factoring a Cubic 125x (5x -2 )(25x 2 +10x +4)