Solving Solving Quadratic Quadratic

Equations By Equations By Graphing Graphing

By: Brielle By: Brielle WoodsWoods

Quadratic EquationsQuadratic Equations

A quadratic equation is a A quadratic equation is a polynomial equation of the polynomial equation of the second degree. The form second degree. The form for a quadratic equation for a quadratic equation is: is: axax22 + bx + c = 0 + bx + c = 0.. The The solutions of a quadratic solutions of a quadratic equation are called equation are called rootsroots..

Two Roots Example Two Roots Example

xx22 + 2x +3 = 0 + 2x +3 = 0 Original equation Original equation Axis of symmetryAxis of symmetry is is or or (-1)(-1)22 + 2(-1) + 3 = 0 + 2(-1) + 3 = 0 Plug in -1 Plug in -1

for “x”for “x” ( -1, 2) ( -1, 2) Coordinates of the VertexCoordinates of the Vertex

1x)1(2

2x

Two Roots Example Two Roots Example (continued)(continued)

Make a table of other points to Make a table of other points to sketch the graph.sketch the graph.

xx f(x)f(x)-2-2 33

-1-1 22

00 33

11 66

22 1111

Two Roots Example Two Roots Example (continued)(continued)

GraphGraph

zz22 + 3z = 18 + 3z = 18 Original ProblemOriginal Problem Subtract 18 from both sides of the Subtract 18 from both sides of the

equation.equation. zz22 + 3z + 3z (– 18) (– 18) = 9 = 9 (-18)(-18) zz2 2 + 3z – 18 = 0+ 3z – 18 = 0 Factor Factor (z - 3)(z + 6) = 0(z - 3)(z + 6) = 0

A Double Root ExampleA Double Root Example

A Double Root Example A Double Root Example (Continued)(Continued)

Zero Product Property Zero Product Property (z - 3) = 0 (z - 3) = 0 Add 3 to both sides of the equation.Add 3 to both sides of the equation. z – 3 z – 3 (+3) (+3) = 0 = 0 (+3)(+3) z = 3z = 3 (z + 6) = 0(z + 6) = 0 Subtract 6 from both sides of the Subtract 6 from both sides of the

equation.equation. z + 6 z + 6 (-6) (-6) = 0 = 0 (-6)(-6) z = -6z = -6 The roots are z = -6 and z = 3The roots are z = -6 and z = 3

Practice ProblemsPractice Problems Solve each equation Solve each equation

by graphing. by graphing. gg22 + 14g + 40 = 0 + 14g + 40 = 0 tt22 + 5t = 25 + 5t = 25 ss22 + 16s + 20 = + 16s + 20 =

00 aa22 + 10a = 30 + 10a = 30 bb22 + 24b + 40 = + 24b + 40 =

00 xx2 2 + 15x = 35+ 15x = 35

zz22 + 26z + 30 + 26z + 30 = 0= 0

ww22 + 20w =40 + 20w =40 yy22 + y +12 = 0 + y +12 = 0 rr22 + r = 25 + r = 25 qq22 + q + 2 = 0 + q + 2 = 0 pp22 + p = 18 + p = 18

Graphic OrganizerGraphic Organizer

Solving Quadratic Solving Quadratic Equations By GraphingEquations By Graphing

2. Find the Axis of

symmetry

3. If the equation equals to

zero factor it out

4. If there is a number on the other side of

the equal side add or subtract that number to both sides of the equation then factor

5. Make a table with other

points to make a correct graph

6. Use the

points to graph

1. Find a,b,c

Answer keyAnswer key1. 2.

3.

Answer keyAnswer key4. 5.

6.

Answer keyAnswer key7. 8.

9.

Answer keyAnswer key10. 11.

12.

Web - ResourcesWeb - Resources

Game:Game: http://www.coolmath.com/calculators/http://www.coolmath.com/calculators/quadratic.htmquadratic.htm

Educational:Educational: http://www.algebra.com/algebra/homehttp://www.algebra.com/algebra/homework/quadratic/ work/quadratic/

Assessment:Assessment: http://www2.wnyric.org/10551049135http://www2.wnyric.org/1055104913545267/lib/1055104913545267/math_st45267/lib/1055104913545267/math_student_handouts_hs.pdf udent_handouts_hs.pdf