Algebraic Expansion
Expand k(7-4k)
7k-4k2
Factorise 9k-k2.
k(9-k)
x2 + 3x – 4 = 0
What is x = –4, x = 1.
Find the vertex of the quadratic function y=-x2-5x+4.
The sum of the squares of two consecutive even integers is 340. Find the two integers.
12 and 14
Expand (x-2)(x+2).
x2-4
Factorise 121-m2.
(11+m)(11-m)
2x2 – 4x – 3 = 0
What is x = –0.58, x = 2.58
Write the quadratic equation in y=a(x-p)(x-q) form that has solutions of -2 and 3.
y=(x+2)(x-3)
George is 5 years older than Harry. If the product of their ages is 234., find Harry's present age.
Harry's present age is 13 years old.
Expand (x-4)(x-6)
Factorise 3x2+13x-10.
(3x-2)(x+5)
9x2 + 12x + 4 = 0
x = –2/3
Write the quadratic equation in y=ax2+bx+c form that passes through points (-2,0), (5,0), and (0,-10).
y=x2-3x-15
A rectangle has dimensons (3x+1) cm by (2x+1) cm. Given that the area of teh rectangle is 117 cm2. Find the perimeter of the rectangle.
The perimeter of the rectangle is 44 cm.
Expand 2x(x2-4)+3x3-6x2+5
5x3-6x2-8x+5
Solve for 7412-2592 without using a calculator.
7412-2592
=(741+259)(741-259)
=(1000)(482)
=482000
3x2 + 4x + 2 = 0.
Write the quadratic function in vertex form, y=a(x-h)2+k, of the graph shown by Ms. Olive
Note: (h,k) is the vertex.
y=-.5(x-1)2+8
A stone is thrown vertically upwards from the top of a cliff. It's height, h metres, above the level ground, can be modelled by h=28+42t-12t2, where t is the time in seconds after the stone has been thrown.
At what time will the stone strike the ground.
At 4.07 sec, the stone will strike the ground.
Expand 2(m+2)(m+1)(m-3)
2m3-14m-12
If 2x2-2y2=125 and x-y=2.5, find the value of x+y.
2x2-2y2=125
2(x2-y2)=125
(x2-y2)=62.5
(x-y)(x+y)=62.5
2.5(x+y)=62.5
x+y=25
Solve (x-2)2+(x+3)2=50
(x-2)2+(x+3)2=50
x2-4x+4+x2+6x+9=50
2x2+2x-37=0 (Use quadratic formula)
x = –4.83, x = 3.83
Write a quadratic function in standard form with the following condition:
1) x-intercepts: 1 negative and 1 positive
2) y-int at (0,8)
3) concave downward
Show your equation to Ms. Olive.
Ricky kicks a soccer ball vertically upwards. the height, h metres, of the ball can be modelled by h=27t-6t2, where t is the time in seconds after it leaves the ground.
Find the maximum height of the ball above the ground and the time at which it occurs.
The ball reaches the height of 30.5 m at 2.25 sec.