Functions
If f(x) = 2x - 10, find f(4).
-2
Multiply (x + 5)(x + 2)
x² + 7x + 10
If two lines in a system have the same slope but different y-intercepts, how many solutions do they have?
Zero / No Solution
Factor: 8x³ + 12x²
4x²(2x + 3)
What formula can be used to find the zeroes of a quadratic if factoring is not possible? (Bonus points if you write the formula correctly)
The quadratic formula
If f(x) = x² and g(x) = 3x, find (f + g)(2).
10
Multiply (x - 4)(x - 6)
x² - 10x +24
Solve using substitution: y = 3x and x + y = 20.
(5, 15)
Factor: x² - 100
(x - 10)(x + 10)
Solve x² = -16 using imaginary numbers.
x = 4i and x = -4i
Given f(x) = 3x - 2 and g(x) = x² + 1, find the value of g(f(2)).
17
Multiply (3x + 1)(x - 5)
3x² - 14x - 5
Solve using elimination: x + y = 12 and x - y = 2
(7, 5)
Factor the trinomial: x² + 7x + 10
(x + 2)(x + 5)
Use the discriminant to determine how many real solutions x² + 4x + 4 = 0 has.
One real solution (discriminant of 0)
If h(x) = √x and g(x) = x+ 4, find h(g(12)).
4
Multiply (x + 4)²
x² + 8x + 16
Solve: 2x + y = 10 and y = -2x + 5.
No Solution — the lines are parallel
Factor the trinomial: x² + 2x - 63
(x + 9)(x - 7)
If a quadratic has roots at x = 3 and x = -2, write its equation in factored form.
y = (x - 3)(x + 2)
If f(x) = 2x² - 3x + 1 and g(x) = x² - 5, find the expression for (f - g)(x).
x² - 3x + 6
Multiply (x - 2)(x² + 2x + 4)
x³ - 8
A system has one equation y = x² and another y = 9. What are the two solutions?
(3, 9) and (-3, 9)
Factor completely: 2x² - 18
2(x - 3)(x + 3)
Use the quadratic formula to find the roots:
x² - 6x + 9 = 0
x = 3