Class Table "Why = a(x - h)² + k?" -- EVERYTHING YOU EVER WANTED TO KNOW ABOUT A QUADRATIC BUT WERE AFRAID TO ASK

Quadratics In General
Solving Quadratics:
· Best Way
· By Factoring
· By Graphing
· By Calculator
· Quadratic Equation, Formula, & The Discriminant
· By Web Page & Formula
· By Completing the Square
· By Spreadsheet
Graphing Quadratics:
· How the general equation y=ax² + bx + c and the standard equation y=a(x-h)² +k relate
· Interactive Graphs of y=ax² + bx + c and y=a(x-h)² +k
· By Point-Plotting
· By Intercepts
· By Inspection or By Using y=a(x - h)² + k
Uses of Quadratics:
· To Create Other Functions
· To Express Projectile Motion
· In Area Problems


The Quadratic, y = ax2 + bx + c
    "Why = a(x - h)2 + k?"
    What?
    y = a(x - h)2 + k
    Bad joke. Let it go.


Quadratic
Quadratic? Quadratic: x2, or 2x2 or -3x2 or ax2.
Quadratic: NOT constant (2, -3, a).
Quadratic: NOT linear (2x or -3x or ax).
Quadratic: NOT cubic (2x3 or -3x3 or ax3).
Quadratic:NOT quartic (-3x4), or higher.

    Quadratics are polynomials where the highest degree of the variable is 2.   Quadratics are polynomials like ax2 + bx + c or a(x - h)2 + k or 2x2 -3x + 5 or 4x2 - 1 or -3x2 + 2x -6.



Uses of Quadratics
    Ok, so now you know what a quadratic expression looks like. What good is it?
    Three uses are discussed here.
  • Quadratics "build" other more complex polynomials or act as factors of more complex polynomials.
     
  • Quadratics are used to express or model projectile or shooting situations.
     
  • Quadratics are used to express or model area situations.


THE Quadratic Equation VS. A Quadratic Equation

    The equation ax2 + bx + c = 0 is the quadratic equation and its solution is . See page The Quadratic Equation, Formula, & Discriminant.

    The equation y = ax2 + bx + c is a quadratic equation because its highest degree is 2.

    It's an equation where a, the coefficient of the quadratic or x2 term, does not equal zero. If a were 0, there would be no quadratic term.

    It's an equation or statement in which y is expressed in terms of a, b, c, and x. Because it's a quadratic, the graph of the curve is a parabola, a quadratic function.

    Quadratic functions are the second simplest of the polynomial functions.

Lines, y= ax + b, are more simple.
Quadratics, y = ax2 + bx + c, are next.
Cubics, y = ax3 + bx2 + cx + d, are next.
Quartics, y = ax4 + bx3 + cx2 + dx + e are next.
Quintics are next.

    In general polynomials look like

y = anxn + an-1xn-1 + an-2xn-2 + ... +a2x2 + a1x1 + a0x0.

    These equations are quadratic: y = ax2 + bx + c or y = a(x - h)2 + k.



Related Pages & Resources

Vocabulary
(axis of) symmetry
concave
discriminant
imaginary
irrational
parabola
quadratic
quadratic formula
vertex
  • The Important Stuff at the Top of the Page


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