LESSON Reteach 5-3 Solving Quadratic Equations by …

1 Name Date ClassReteachSolving Quadratic Equations by Graphing and Factoring5-3 LESSONS olve the equation a x 2 bx c 0 to find the roots of the the roots of x 2 2x 15 0 to find the zeros of f x x 2 2x 15. x 2 2x 15 0 x 5 x 3 0 x 5 0 or x 3 0x 5 or x 3To check the roots, substitute each root into the original equation:Equation: x 2 2x 15 0 x 2 2x 15 0 Root: x 5 x 3 Check.

2 5 2 2 5 15 3 2 2 3 15 25 10 15 0 9 6 15 0 The roots of x 2 2x 15 0 are 5 and zeros of f x x 2 2x 15 are 5 and the zeros of each function by factoring. Set the function equal to 0, factor, set each factor equal to 0, and then solve each equation. x 4 x 2 24x x x 2 4x 3 4 x 2 24x 0 x 2 4x 3 0 4x x 6 0 x 3 x 1 04x 0 or x 6 0 x 3 0 or x 1 0x 0 or x 6 x 3 or x 1 x x 2 5x 4 x 3 x 2 12x x 2 5x 4 03 x 2 12x 0 x 4 x 1 03x x 4 0x 4 0 or x 1 03x 0 or x 4 0x 4 or x 1x 0 or x 4 Factor.

3 Then multiply to each equation for each factor equal to roots of the equation are the zeros of the by Holt, Rinehart and Winston. 22 Holt Algebra 2 All rights 2212/20/05 3:14:52 PM12/20/05 3:14:52 PMProcess BlackProcess BlackName Date ClassLESSON5-3 ReteachSolving Quadratic Equations by Graphing and Factoring (continued)Some Quadratic Equations have special of Two Squares: a 2 b 2 a b a b Perfect Square Trinomials.

4 A 2 2ab b 2 a b 2 a 2 2ab b 2 a b 2 Always write a Quadratic equation in standard form before factoring. 16 x 2 25 16 x 2 25 0 4x 2 5 2 0 4x 5 4x 5 0 4x 5 0 or 4x 5 0 x 5 __ 4 or x 5 __ 4 Try to factor a perfect square trinomial if the coefficient of x and the constant term are perfect squares.

5 4 x 2 12x 9 0 2x 2 2 2x 3 3 2 0 2x 3 2x 3 2x 3 2 0 2x 3 0 x 3 __ 2 Find the roots of each equation by factoring. 5. 4 x 2 49 6. x 2 16 8x 4 x 2 49 0 x 2 8x 16 0 2 x 2 7 2 0 x 2 2 4 x 4 2 0 2x 7 2x 7 0 x 4 2 0 2x 7 0 or 2x 7 0 x 4 0 x 7 __ 2 or x 7 __ 2 x 416 and 25 are perfect squares.

6 Use the difference of two squares to each factor equal to x 2 and 9 are perfect factors are the by Holt, Rinehart and Winston. 23 Holt Algebra 2 All rights 2312/15/05 4:36:46 PM12/15/05 4:36:46 PMProcess BlackProcess BlackCopyright by Holt, Rinehart and Winston. 79 Holt Algebra 2 All rights reserved.#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL RIGHTS RESERVED ,%33/.x * >V Vi 3 OLVING 1 UADRATIC %QUATIONS BY 'RAPHING AND &ACTORING4 ELL WHETHER EACH STATEMENT IS TRUE OR FALSE 1 UADRATIC FUNCTIONS HAVE ONLY ONE ZERO &ALSE !))

7 ZERO OF A FUNCTION IS THE VALUE OF X THAT MAKES F S X D 4 RUE 4HE POINTS S D AND S D COULD BE THE ZEROS OF A GIVEN Quadratic FUNCTION &ALSE&IND THE ZEROS OF F T X E X X BY USING A TABLE AND A GRAPH )N WHAT DIRECTION DOES THE PARABOLA OPEN 5 PWARD &IND THE Y INTERCEPT &IND THE VERTEX T E 0 LOT THE VERTEX AND THE Y INTERCEPT #OMPLETE THE TABLE AND USE THE VALUES TO DRAW THE GRAPH 7 HAT ARE THE ZEROS OF THE FUNCTION AND &IND THE ZEROS OF EACH FUNCTION BY FACTORING F S X D X X A 3ET THE FUNCTION EQUAL TO X X B &ACTOR S X D S X D C 3ET EACH FACTOR EQUAL TO S X D OR S X D D 3 OLVE EACH EQUATION FOR X X OR X F S X D X 3 OLVE !

8 Quadratic FUNCTION HAS ZEROS EQUAL TO AND A 7 HAT IS THE FACTORED FORM OF THE FUNCTION T X E T X E B -ULTIPLY THE FACTORS TO GIVE THE Quadratic FUNCTION X X XY X F S X D #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON }iL > !LL RIGHTS RESERVED --" x * >V Vi 3 OLVING 1 UADRATIC %QUATIONS BY 'RAPHING AND &ACTORING&IND THE ZEROS OF EACH FUNCTION BY USING A GRAPH AND A TABLE F S X D X X X F S X D > ` G S X D X X X F S X D > ` x&IND THE ZEROS OF EACH FUNCTION BY FACTORING H S X D X X F S X D X X G S X D X X x] { x] {&IND THE ROOTS OF EACH EQUATION BY FACTORING X X X x])}

9 X7 RITE A Quadratic FUNCTION IN STANDARD FORM FOR EACH GIVEN SET OF ZEROS AND AND F T X E X xX { F T X E X X n3 OLVE 4HE Quadratic FUNCTION THAT APPROXIMATES THE HEIGHT OF A JAVELIN THROW IS H S T D T WHERE T IS THE TIME IN SECONDS AFTER IT IS THROWN AND H IS THE JAVELIN S HEIGHT IN FEET (OW LONG WILL IT TAKE FOR THE JAVELIN TO HIT THE GROUND L x XY #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL RIGHTS RESERVED ,%33/.* >V Vi 3 OLVING 1 UADRATIC %QUATIONS BY 'RAPHING AND &ACTORINGx &IND THE ZEROS OR ROOTS OF EACH FUNCTION OR EQUATION F S X D X X G S X D X X X X X ?)))}

10 ? ?? 3 OLVE &IND THE ZEROS OF H S X D X X BY GRAPHING ?? 7 RITE A Quadratic FUNCTION IN STANDARD FORM WITH ZEROS AND F T X E X X 7 RITE AN EQUATION IN STANDARD FORM WITH ROOTS AND F T X E X X 7 RITE A Quadratic FUNCTION WITH TWO ZEROS THAT HAVE A SUM OF &OR ROOTS AND F T X E X X 7 RITE A Quadratic EQUATION WITH JUST ONE NONZERO ROOT F T X E X X3 OLVE A -ARILYN HIT A GOLF BALL ON THE GROUND WITH HER DRIVER 5SE THE GENERAL FUNCTION FOR A PROJECTILE TO WRITE A FUNCTION THAT SHOWS THE HEIGHT IN FEET OF HER GOLF BALL AS A FUNCTION OF TIME 4HE BALL WAS HIT WITH AN INITIAL VERTICAL