Page 1 â€¢Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c â€¢The constants are: a , b, c â€¢The variables are: y, x Page 2 â€¢Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c â€¢The constants are: a , b, c â€¢The variables are: y, x â€¢The ROOTS (or solutions) of a polynomial are its x-intercepts â€¢Recall: The x- intercepts occur where y = 0. Roots Page 3 â€¢Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c â€¢The constants are: a , b, c â€¢The variables are: y, x â€¢The ROOTS (or solutions) of a polynomial are its x-intercepts â€¢Recall: The x- intercepts occur where y = 0. Roots â€¢Example: Find the roots: y = x 2 + x - 6 â€¢Solution: Factoring: y = (x + 3)(x - 2) â€¢0 = (x + 3)(x - 2) â€¢The roots are: â€¢x = -3; x = 2 Roots Page 4 â€¢Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c â€¢The constants are: a , b, c â€¢The variables are: y, x â€¢The ROOTS (or solutions) of a polynomial are its x-intercepts â€¢Recall: The x- intercepts occur where y = 0. Roots â€¢Example: Find the roots: y = x 2 + x - 6 â€¢Solution: Factoring: y = (x + 3)(x - 2) â€¢0 = (x + 3)(x - 2) â€¢The roots are: â€¢x = -3; x = 2 Roots â€¢But what about NASTY trinomials that donâ€™t factor? â€¢Abu Ja'far Muhammad ibn Musa Al-Khwarizmi â€¢Born: about 780 in Baghdad (Iraq) â€¢Died: about 850 Page 5 â€¢Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c â€¢The constants are: a , b, c â€¢The variables are: y, x â€¢The ROOTS (or solutions) of a polynomial are its x-intercepts â€¢Recall: The x- intercepts occur where y = 0. Roots â€¢Example: Find the roots: y = x 2 + x - 6 â€¢Solution: Factoring: y = (x + 3)(x - 2) â€¢0 = (x + 3)(x - 2) â€¢The roots are: â€¢x = -3; x = 2 Roots â€¢But what about NASTY trinomials that donâ€™t factor? â€¢Abu Ja'far Muhammad ibn Musa Al-Khwarizmi â€¢Born: about 780 in Baghdad (Iraq) â€¢Died: about 850 â€¢After centuries of work, mathematicians realized that as long as you know the coefficients, you can find the roots of the quadratic. Even if it doesnâ€™t factor! y ? ax 2 ?bx ? c, a ? 0 x ? ?b ? b 2 ? 4ac 2aRead More

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