Solving Quadratic Equations By Graphing By: Brielle Woods

Quadratic Equations A quadratic equation is a polynomial equation of the second degree. The form for a quadratic equation is: ax2 + bx + c = 0. The solutions of a quadratic equation are called roots.

Two Roots Example x 2 + 2x +3 = 0 Original equation x 2 + 2x +3 = 0 Original equation Axis of symmetry is or Axis of symmetry is or Axis of symmetry Axis of symmetry (-1) 2 + 2(-1) + 3 = 0 Plug in -1 for “x” (-1) 2 + 2(-1) + 3 = 0 Plug in -1 for “x” ( -1, 2) Coordinates of the Vertex ( -1, 2) Coordinates of the Vertex

Two Roots Example (continued) Make a table of other points to sketch the graph. Make a table of other points to sketch the graph. xf(x)

Two Roots Example (continued) Graph Graph

z 2 + 3z = 18 Original Problem z 2 + 3z = 18 Original Problem Subtract 18 from both sides of the equation. Subtract 18 from both sides of the equation. z 2 + 3z (– 18) = 9 (-18) z 2 + 3z (– 18) = 9 (-18) z 2 + 3z – 18 = 0 z 2 + 3z – 18 = 0 Factor Factor (z - 3)(z + 6) = 0 (z - 3)(z + 6) = 0 A Double Root Example

A Double Root Example (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 (+3) = 0 (+3) z – 3 (+3) = 0 (+3) z = 3 z = 3 (z + 6) = 0 (z + 6) = 0 Subtract 6 from both sides of the equation. Subtract 6 from both sides of the equation. z + 6 (-6) = 0 (-6) z + 6 (-6) = 0 (-6) z = -6 z = -6 The roots are z = -6 and z = 3 The roots are z = -6 and z = 3

Practice Problems Solve each equation by graphing. Solve each equation by graphing. g g + 40 = 0 g g + 40 = 0 t 2 + 5t = 25 t 2 + 5t = 25 s s + 20 = 0 s s + 20 = 0 a a = 30 a a = 30 b b + 40 = 0 b b + 40 = 0 x x = 35 x x = 35 z z + 30 = 0 w w =40 y 2 + y +12 = 0 r 2 + r = 25 q 2 + q + 2 = 0 p 2 + p = 18

Graphic Organizer Solving Quadratic Equations 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 key

Answer key

Answer key

Answer key

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