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

    "Why = a(x - h)² + k?"

    What?

    y = a(x - h)² + k

    Bad joke. Let it go.

    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.

    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 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 = a_nxⁿ + a_n-1x^n-1 + a_n-2x^n-2 + ... +a₂x² + a₁x¹ + a₀x⁰.

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

• Squaring and Square Root Functions
   
• Quadratic Equation, Formula, & The Discriminant
   
• Why A Quadratic Looks/Behaves in a Certain Way

Vocabulary

(axis of) symmetry

concave

discriminant

imaginary

irrational

parabola

quadratic

quadratic formula

vertex

• The Important Stuff at the Top of the Page