 "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 