Page 1 •Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c •The constants are: a , b, c •The variables are: y, x Page 2 •Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c •The constants are: a , b, c •The variables are: y, x •The ROOTS (or solutions) of a polynomial are its x-intercepts •Recall: The x- intercepts occur where y = 0. Roots Page 3 •Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c •The constants are: a , b, c •The variables are: y, x •The ROOTS (or solutions) of a polynomial are its x-intercepts •Recall: The x- intercepts occur where y = 0. Roots •Example: Find the roots: y = x 2 + x - 6 •Solution: Factoring: y = (x + 3)(x - 2) •0 = (x + 3)(x - 2) •The roots are: •x = -3; x = 2 Roots Page 4 •Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c •The constants are: a , b, c •The variables are: y, x •The ROOTS (or solutions) of a polynomial are its x-intercepts •Recall: The x- intercepts occur where y = 0. Roots •Example: Find the roots: y = x 2 + x - 6 •Solution: Factoring: y = (x + 3)(x - 2) •0 = (x + 3)(x - 2) •The roots are: •x = -3; x = 2 Roots •But what about NASTY trinomials that don’t factor? •Abu Ja'far Muhammad ibn Musa Al-Khwarizmi •Born: about 780 in Baghdad (Iraq) •Died: about 850 Page 5 •Intro: We already know the standard form of a quadratic equation is: y = ax 2 + bx + c •The constants are: a , b, c •The variables are: y, x •The ROOTS (or solutions) of a polynomial are its x-intercepts •Recall: The x- intercepts occur where y = 0. Roots •Example: Find the roots: y = x 2 + x - 6 •Solution: Factoring: y = (x + 3)(x - 2) •0 = (x + 3)(x - 2) •The roots are: •x = -3; x = 2 Roots •But what about NASTY trinomials that don’t factor? •Abu Ja'far Muhammad ibn Musa Al-Khwarizmi •Born: about 780 in Baghdad (Iraq) •Died: about 850 •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 doesn’t factor! y ? ax 2 ?bx ? c, a ? 0 x ? ?b ? b 2 ? 4ac 2aRead More