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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