html5-img
1 / 12

Algebra 2

Algebra 2. Section 4.7 Complete the Square Section 4.8 Quadratic Formula and the Discriminant. 4.7 Complete the Square . Standard Form ax 2 + bx + c Intercept Form m(x - p)(x - q) Vertex Form m(x -d) 2 + b. Example 1: 4.7.

clive
Télécharger la présentation

Algebra 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Algebra 2 Section 4.7 Complete the Square Section 4.8 Quadratic Formula and the Discriminant

  2. 4.7 Complete the Square • Standard Form ax2 + bx + c • Intercept Form m(x - p)(x - q) • Vertex Form m(x -d)2 + b

  3. Example 1: 4.7 • Write y = x2 + 14x + 44 in vertex form. Then identify the vertex. Step 1: Complete the square (find c) 14/2 = 7 7*7 = 49 = c Step 2: Add c to both sides of the equation. y + 49 = x2 + 14x + 49 + 44 Step 3: Factor only your perfect square trinomial y + 49 = (x + 7)2 + 44 Step 4: Solve for y. y = (x + 7)2 + 44 - 49 y = (x + 7)2 - 5 (-7, -5)

  4. Assignment: Page 288 #36 • Find the value of x. Area of a parallelogram = 48 A = bh 48 = (x + 6)x 48 = x2 + 6x Step 1: complete the square 48 + 9 = x2 + 6x + 9 Step 2: factor and solve 57 = (x + 3)2 x x + 6

  5. Assignment: Page 289 #44 Write the quadratic function in vertex form. Then identify the vertex. y = x2 + 20x + 90 Step 1: complete the square 20/2 = 10, 10*10 = 100 = c Step 2: add c to both sides y + 100 = x2 + 20x + 100 + 90 Step 3: factor only perfect square trinomial y + 100 = (x + 10)2 + 90 Step 4: solve for y y = (x + 10)2 + 90 - 100 y = (x + 10)2 - 10 Vertex: (-10,-10)

  6. Assignment: Page 289 # 48 - 52 eoe You have 5 minutes!

  7. 4.8 The Quadratic Formula and the Discriminant • Standard Form: ax2 + bx + c • Quadratic Formula: formula that solves any quadratic equation • Discriminant: b2 - 4ac

  8. Discriminant: will tell you the number of solutions • When b2 - 4ac > 0, then the equation has two solutions and the graph has 2 x-intercepts • When b2 - 4ac = 0, then the equation has one solution and the graph has 1 x-intercept • When b2 - 4ac < 0, then the equation has two imaginary solutions and the graph has no x-intercepts

  9. two solutions Example 1: • Solve x2 + 7x = 6 Step 1: put equation in standard form x2 + 7x = 6 -6 -6 x2 + 7x - 6 = 0 Step 2: label a, b, and c a = 1, b = 7, c = -6 Step 3: Plug and Chug

  10. one solution Example 2: • Solve 2x2 - 8x + 8 = 0 Step 1: Standard form Already in it! Step 2: label a, b, and c a = 2, b = -8, c = 8 Step 3: Plug and Chug

  11. imaginary solutions Example 3: • Solve -x2 + 2x = 5 Step1: standard form -x2 + 2x = 5 -5 -5 -x2 + 2x - 5 = 0 Step 2: label a, b, and c a = -1, b = 2, c = -5 Step 3: Plug and Chug

  12. Assignment: Page 288 and 296 • # 36, 44 - 52 eoe • # 4 - 60 eoe

More Related