College Algebra Ch.3

Front 1

Solving a quadratic function
f(x)=a(x-h)^2 +k

Back 1

(h,k)=vertex
If a>0, the parabola opens up
If a<0, the parabola opens down
x-intercepts: solve for x by setting f(x) equal to zero.
y-intercepts: plug in f(0). Solve.

Front 2

Solving a quadratic equation
(general form)
f(x)=ax^2+bx+c

Back 2

Vertex=-b/2a, then f(-b/2a)
If a>0, the parabola opens up
If a<0, the parabola opens down
x-intercepts: factor
y-intercepts: plug in F(0). Solve.

Front 3

Zeros

Back 3

x-intercepts. Factor (solve) to get answer.

Front 4

The quadratic formula

Back 4

x=(-b-√b^2-4ac)/2a

x=(-b+√b^2-4ac)/2a

Note: Factors ALL the time.

Front 5

Multiplicities

Back 5

Exponents, usually the highest in an equation.

Front 6

Rational function

Back 6

P(x)/Q(x)

Front 7

Domain/vertical asymptotes of a rational function

Back 7

Solve by factoring the denominator, then solving the result. If the denominator cannot be factored, then the domain is infinite and there are no vertical asymptotes.

Front 8

Cost function

Back 8

C(x)=(fixed cost)+[(cost per unit x units produced)] ALL divided by units produced

Front 9

Solving polynomial inequalities

Back 9

1. Solve equation (factor)
2. Graph points on number line
3. Plot boundary points beside graphed points.
4. Plug boundary points into original equation. If the plugged in points make the inequality statement false, then the line does not advance in the direction of said boundary point. Brackets are only used when there is an equal sign involved.

Front 10

Solving rational inequalities

Back 10

1. Solve the numerator and denominator to get your points.
2. Use same methods as regular polynomial inequalities.