VOCABULARY
a2 - b2 = (a + b)(a - b) is called the ____________ __ __________ identity.
difference of squares
Factor the following:
a2 + 6ab + 9b2 - 49
(a +3b)2 - 49
What is the sum of all the roots of this equation?
7x2 = 49x
7
If the area of a rectangle can be expressed as 2x2 + 11x - 21, and the width of the rectangle is (x + 7), what is the expression that could represent its length?
2x - 3
What are the roots of the equation
1/x2 + 1/x - 20 = 0?
x = -1/5 or x = 1/4
Expressions in the form of..
ax2 +bx + c
are called?
Quadratic Expressions (or just quadratics)
Factor the following:
4a2 - 20ab +25b2 - 100
(2a - 5b + 10)(2a - 5b - 10)
What are the solutions to the equation x2 = 4?
2, -2
The height of a triangle is 7 less than its base. If the area of the triangle is 225, what is its height?
18
If bx2 + 32x = 4x(x - a), what is the value of ab?
-32
FOIL(ing) is the reverse of ______________
Factoring
If the following statement is true, what is the value of a?
x2 + 5x - 14 = (x + a)(x - 2)
7
What are the roots of the quadratic equation..
2(x+2)2 - 33 = 13x + 8?
x = -3 OR x = 11/2
In 20 years, Fred will be half the square of the age he was 4 years ago. How old is Fred now?
12
7 days
The shape of graph that a quadratic function makes is called a _______________.
parabola
If x2 - 8x + 15 = (x + a)(x + b), what is the value of ab?
15
10
When the square of a certain positive integer is reduced by 38, we get a value of 83. What is the integer?
11
Cole brings home 100kg of potatoes, which consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight?
50kg
If you have a quadratic equation that you cannot factor using normal methods, you might have to use this complicated formula...
quadratic formula
Factor the following:
4x3 + 24x2 + 27x - 28
(2x +7)(2x2 + 5x - 4)
If a rectangle had a length of 6 - x and a width of x + 8, what would be its largest possible area?
49
Suppose that 6 is one of the roots of the quadratic equation x2 - 2x + a = 0. What is the other root?
-4
x(y + z) = 39
y(x + z) = 60
z(x + y) = 63
x2 + y2 + z2 = ?
94