Download MPM2D1 - Sklepowicz

MPM2D1
Date: DUE TUES JAN 7
OPTIONAL EXTRA CREDIT ASSIGNMENT
**Answer the following questions on a separate sheet of paper
Quadratics
1. Expand
a) (2x + 5)2
b) (2x – y)(x + 3y)
c)
y=
1
2
( x + 3) - 4
2
2. Write the following equations in factored form and state the zeros.
a) y = 2x2 + 4x
b) y = x2 –x–6
c) y = 2a2 + 11a + 5
d) y = 4x2 – 25
3. Determine the coordinates of the vertex by completing the square.
a) y  x  4 x  2
b) y  2 x  12 x  15
2
2
4. Solve
a) x2 + 10x + 16 = 0
b) x2 + x – 4 = 0
c) –4.9t2 + 50t + 1.5 = 0
5. A model rocket is launched from the roof of a building. Its flight path through the air is modelled by h  5t  30t  10 ,
where h is the height of the rocket above the ground in metres and t is the time after the launch in seconds.
2
(a) At what time will the rocket hit the ground?
(b) How many metres above the ground was the rocket before it took off?
(c) What is the rocket’s maximum height, and after how long does that height occur?
Co-ordinate Geometry
6.
Determine the equation of the perpendicular bisector of the line through the points Q (5, 8) and R (-1, 2).
Verifying Geometric Shapes
7.
A triangle has vertices A (-1, 3), B (1, 7), and C (5, 5).
a)
Verify that ΔABC is a right triangle.
b) Determine whether the triangle is scalene, isosceles, or equilateral.
c)
Using the grid on the right, find a point D so that ABCD is a square.
d) Verify that ABCD is a square.
Linear Systems
8.
Solve the following algebraically (i.e. by substitution or elimination).
a)
y = 3x
2x – 4y = 30
b)
(Graph the equations
on the grid provided to check your answers)
2x – 3y = 5
x + 6y = –5