A straight line passes through the two points A and B with coordinates A(–3,–5) and B(5,1).

a) Determine an equation for the line

Problem 6: roots of quadratic equations

The following quadratic equations have been factorized for you. Read off the roots:

a. x2 – 40x + 300 = (x–10)(x–30) = 0

b. x2 + x – 1 = (x–½)(x+2) = 0

c. x2 – (+)x + = (x–)(x–) = 0

d. 6x2 + 6x – 72 = (2x–6)(3x+12) = 0

Factorise, and hence determine the roots of the quadratic equation:

e. x2 + 5x + 6 = 0

f. x2 + 6x – 7 = 0

Problem 7: throwing up…

A ball is thrown into the air. The height (over the ground, in metres) of the ball is called y, and a formula for y is y = . Here g denotes the acceleration of gravity, g = 9.8 m/s2, t is the time from when the ball is thrown (in seconds), and v is the speed with which the ball is thrown (in m/s).

a) With your graphing calculator, sketch y as a function of t for a ball thrown upwards with the speed v = 5 m/s. Copy the graph onto paper.

b) With your calculator, find the maximum height the ball reaches (2 sig. figs.)

c) After how many seconds is the ball back on the ground? (2 sig. figs.)