Lesson's Content
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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.
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.
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