# Quadratic Functions. Graphing and Finding the roots, zeros, or solutions.

### Fantastic lesson that presents quadratic functions (parabola) with all the possible solution paths that we may use to graph it, or to find the solutions. It shows how to find the vertex form of the parabola equation from the graph and from a set of coordinate points. While challenging, it is simply put. Simple!

Lesson's Content

 Lesson In PDF Format (no animations)

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.

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.

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 = 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.

Square Root: If x2 = y, then x is the square root of y. Square root is the opposite of square.

Solution or root: The value that makes an equation a true statement, a root refers particularly to the value of x for which y = 0, this value is also the x-intercept of the graph.

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).

Zeros of a function: The solutions for the equation of the function when this equal to 0. The roots, also known as the x-intercepts.

Interactive Algebraic Applets

A quadratic function has features like the axis of symmetry, vertex, and x-intercepts,

or zeros. You find the axis of symmetry, and then with that value for x, you find

the y-coordinate for the vertex. Once you have these, then you may use Quadratic

Formula to find the x-intercepts. This interactive algebraic applet allows you

to drag slides for parameters a, b, and c; while you do it the applet update

values for the process above explained.

A second degree function has its features: Axis of symmetry, vertex, and x-intercepts,

or zeros. You may find the axis of symmetry, and then with that value for x, you proceed to

find the y-coordinate for the vertex. Once you have these, then you may complete

the square to find the x-intercepts. This interactive algebraic applet allows you

to drag slides for parameters a, b, and c; while you do it the applet update

values for the process above explained.

Vocabulary Puzzle

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