HPC1.1/1.2/A.3 Notes

Learning Targets: - Use the distance formula- Use the midpoint formula

- Transfer algebraic information into graphic information- Completely factor polynomials

Do you remember these formulas: Distance and Midpoint?

Distance =

Midpoint =

Ex 1) Find the distance between (6, 0) & (-3, 2)

Ex 2) Find the midpoint of the line segment joining (-4, -3) & (2, 2).

Ex 3) Find all points have a y-coordinate of -3 whose distance from the point (1, 2) is 13.

Ex 4) Find all points on the x-axis that are 5 units from the point (4, -3).

Ex 5) Given the equation

• (a) Determine whether (3, 5) is on the graph.

• (b) If (1, b) is on the graph, what is b?

2( ) ( 1) 9f x x

Ex 5) Given the equation

• (c) Algebraically determine the x- and y- intercepts.

• (b) Graph f(x) on your calculator and then determine the intercepts.

2( ) ( 1) 9f x x

Factoring: Sums/Differences of Cubes

• Difference of 2 cubes:

• Sum of 2 cubes:

3 3 2 2x a x a x ax a

3 3 2 2x a x a x ax a

Ex 6) Factor each completely

(a) (b)

(c) (d)

3 27x 4 1x

29 12 4x x 3 24 2 8x x x