Methods to Solving the Quadratic Equation Foldable

1. Methods to Solving the Quadratic Equation Foldable Another Snow day! More foldables! Relax about the quadratic equation. There are so many ways to solve it. Created by Ms.Nhotsoubanh

2. Materials you will need… • Construction Paper (soft colors) or computer paper • Scissors • Markers (2 to 3 Dark colors) • Pen or Pencil • ruler

3. Directions: • Lay your construction horizontally so that we are folding the 17 inches in half. • We want the largest viewing area as possible. • Fold your construction paper in half, vertically down the middle (taco style). • Fold both ends of the construction paper inward so that they meet at the center crease.

4. Heading • Using a ruler, measure approximately one and a half inches from the top and mark it. • Do the same for the other side. • Cut off the piece from both sides. Do not cut too much. • This will be front of your foldable; your heading will be displayed here.

5. Methods to solving Quadratic Equations • Using one of your markers, write “Methods to Solving Quadratic Equations”in the top as your heading. • Measure about 5 inches from the top and mark both sides of the front cover. • Using your scissors, cut to the first crease. DO NOT CUT ALL THE WAY. (cut along the red lines) • The foldable should start taking form. scrap scrap

6. Methods to Solving Quadratic Equations Factoring by x-Box Square Root Principle Quadratic Formula Sections • Close the flaps so that you can see the front of your cover; you should see 4 individual parts. • Using a marker, label each part as follows: • Factoring by Grouping • Factoring by x-Box • Quadratic Formula • Square Root Principle Factoring by Grouping

7. Methods to solving Quadratic Equations By Grouping: Your turn Your turn By x-Box: cut in half cut in half By the Quadratic Formula: Example 3 Your turn Your turn By Square Root Principle: Example 4 THIS IS HOW YOUR FOLDABLE WILL LOOK WHEN IT IS COMPLETED Example 1 Example 2

8. By Grouping: a(c) Factors of a(c) that will give you b b Standard form for a quadratic equation is ax2 + bx + c = 0 a(c) Example 1: Solve: 5x2 + 7x – 6 = 0 Your turn: Solve: 3x2– 12x – 15 = 0 -30 -3 10 1st term last term b ( ) ( ) + 10x 7 5x2 – 8 = 0 – 3x Factor out gcf for each binomial x(5x – 3) + 2(5x – 3) = 0 (x + 2) (5x – 3) = 0 Solve for x x + 2 = 0 5x – 3 = 0 +3 +3 5x = 3 5 5 x = x = -2 x = { -2, }

9. By x-Box Standard form for a quadratic equation is ax2 + bx + c = 0 a(c) Example 2: Solve: 5x2 + 7x – 6 = 0 Your turn: Solve: 3x2– 12x – 15 = 0 -30 -3 10 b x +2 7 1stTerm Factor Place the factors: 10 & -3 in the box and add an x to each 5x 5x2 +10x Factor Last term Then factor out gcf for each binomial -3 -3x -6 (x + 2) (5x – 3) = 0 Solve for x x + 2 = 0 5x – 3 = 0 +3 +3 5x = 3 5 5 x = x = -2 x = { -2, }

10. By the Quadratic Formula Standard form for a quadratic equation is ax2 + bx + c = 0 Example 3: Solve: 5x2 + 7x – 6 = 0 Your turn: Solve: 3x2– 12x – 15 = 0 a = _____ b = _____ c = ___ 5 7 -6 Steps: 1. Define a, b, and c. 2. Write the quadratic formula. 3. Substitute the given values into the formula. 4. Solve for x. (you should have 2 answers) x = { -2, }

11. By the Square Root Principle Standard form for a quadratic equation is ax2 + bx + c = 0 Example 4: Solve: 2x2 – 32 = 0 Here is the exception, when there is no “b”, you get: ax2 + c = 0 Steps: Your turn: 3x2 – 27 = 0 2x2 – 32 = 0 1.Isolate the x2 term. +32 +32 2x2= 32 2 2 2. Take the square root of both sides (that gets rid of the “square”, just like when solving radical equations) x2 = 16 3. Solve for x. (you should have 2 answers)

12. There’s another method to solve for the zeros of a quadratic equation……… Graphing! You’ll find out how tomorrow.