Conic Sections - Ellipse
standard form of the equation of an ellipse:
Algebra
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http://course-notes.org/Algebra
Conic Sections - Parabola
Standard Equation: x<sup>2</sup>= 4py y<sup>2</sup>= 4px
vertical parabola horizontal parabola
axis y-axis x-axis
vertex (0,0) (0,0)
p is the focus of p>0 opens up p>0 opens right
the parabola
p<0 opens down p<0 opens left
focus (0,p) (p,0)
Conic Sections - Circles
Consider two points C(h,k) and P(x,y) ;and the distance between them is r. From the distance formula:
Parallel and Perpendicular Lines
Slope-Intercept Form
Slope of a Line
If P1(x1, y1)and P2(x2, y2)are two different points, then the slope of the line between them is;
The Quadratic Formula
ax2+ bx + c = 0
The quadratic formula is used to solve unfactorable quadratic equations.
Quadratic Inequalities
The general forms for quadratic inequalities are:
ax2+ bx + c > 0
ax2+ bx + c < 0
ax2+ bx + c >= 0
ax2+ bx + c =< 0
The number line plays an important role in solving factorable quadratic inequalities.
Quadratic Equations
Quadratic Equations (2nd degree equations in one variable. )
Standard form is ax²+ bx + c.
Rationalizing the Denominator
Since a rational expression is the quotient of two algebraic expressions, it can be represented in fractional form. In doing so, it is often desirable to eliminate all terms involving radicals from the denominator of the fraction. This is known as rationalizing the denominator.
EX.
Quadratic Expressions
The quadratic expressions considered herein are of the form
ax2 + bx + c
where x is the (only) variable, and a, b and c are nonzero real numbers.
When a = 1, the quadratic expression simplifies to
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