Parabolas. Learning to Graph Them From The Equation. Getting The Equation From The Graph.

You are given a long equation that has x's and y's and you are supposed to graph a parabola out of it, but how? They give you the graph of a parabola and you have to get the equation? How should a parabola equation that has y to the second power, rather than x to the second power be treated? ... I have never worked horizontal parabolas! I know that I have to complete the square but the steps are confusing!

This lesson takes the pain out of it. You will be walked in a methodical step by step process: going from simple to complex; giving you plenty of examples covering all the different cases you may have to confront in an hypothetical assignment. You should really try it!

Lesson's Content

Lesson's Glossary

Axis of Symmetry: A line on which a graph is reflected onto itself.

Completing the Square: Method that finds the constant term in an incomplete perfect square trinomial of a second degree equation to solve it.

Conic section: A figure that is obtained slicing a double cone with a plane. (parabola, circle, hyperbola, and ellipse)

Factoring: The process to brake a polynomial down into the product of several factors.

Factors: All whole numbers that are multiplied together to yield another number.

Factored Form: Any polynomial that is written as the product of polynomials of lower degree that may be obtained from the original polynomial.

Function: A relation of the type that has exactly one value in the domain (independent variable) matching a value in the range (dependent variable).

Function notation: A function written with the symbol f(x) instead of y. It is read as f of x.

Parabola: The u curved shape you get when graphing a quadratic equation.

Quadratic equation: An equation of the form

ax2 + bx + c = 0 where a, b, and c are real numbers and a is different from zero.

Quadratic formula: If ax2 + bx + c =0 and a is different from zero then the quadratic formula is given in terms of a, b, and c.

Quadratic function: Any function in the form of

f(x) = ax2 + bx + c where a is different from zero. The graph is a parabola and the largest exponent is 2.

Vertex: The lowest point for a parabola that opens up (minimum); the highest point for a parabola that opens down (maximum).

Vertex form of a quadratic function: The vertex form of a quadratic function is: f(x) = a(x-h)2 + k. The vertex coordinates are (h,k).

Interactive Algebraic Applets

Parabolas have focus, vertex, axis of symmetry, directriz, and latus rectum.

They may be vertical, or horizontal parabola. In this interactive applet you will be able

to explore a vertical parabola; by changing the parameters of the vertex formula.

All you have to do is to drag the sliders for a, h, and k. You will get all the

associated equations instantly updated.

Vocabulary Puzzle

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