PARABOLA FORMULA PROOF.

Have you wondered how is it that the formula for the parabola was obtained? In this lesson you will have the opportunity to see that using the definition for the parabola and the distance formula: You may determine a way of setting up an equation that when simplified gives you the formula of the parabola centered in the origin with parameters (h,k) the coordinates of the vertex in (0,0). After that then we apply a translation with values different than h=0, anb k=0. In effect applying a tranlation vector with h horizontal units of translation and k vertical units of translation which allow us to move the parabola to the four quadrants in the coordinate plane. For example if h<0, and K>0 we translate it to the second quadrant.

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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).

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