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Converting Quadratic Equations

Converting Quadratic Equations. A step-by-step guide with practice. Intercept Form to Standard Form. Write the equation in standard form: y = – 2(x + 3)(x – 2). Intercept Form to Standard Form. Write the equation in standard form: y = – 2(x + 3)(x – 2)

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Converting Quadratic Equations

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  1. Converting Quadratic Equations A step-by-step guide with practice

  2. Intercept Form to Standard Form • Write the equation in standard form: • y = – 2(x + 3)(x – 2)

  3. Intercept Form to Standard Form • Write the equation in standard form: • y = – 2(x + 3)(x – 2) • y = – 2(x2 + x – 6) multiply binomials

  4. Intercept Form to Standard Form • Write the equation in standard form: • y = – 2(x + 3)(x – 2) • y = – 2(x2 + x – 6) multiply binomials • y = – 2x2 – 2x + 12 distribute

  5. Vertex Form to Standard Form • Write this equation in standard form: • y = 2(x – 3)2 + 4

  6. Vertex Form to Standard Form • Write this equation in standard form: • y = 2(x – 3)2 + 4 • y = 2(x2 – 6x + 9) + 4 square the binomial by using foil

  7. Vertex Form to Standard Form • Write this equation in standard form: • y = 2(x – 3)2 + 4 • y = 2(x2 – 6x + 9) + 4 square the binomial by using foil • y = 2x2 – 12x + 18 + 4 distribute

  8. Vertex Form to Standard Form • Write this equation in standard form: • y = 2(x – 3)2 + 4 • y = 2(x2 – 6x + 9) + 4 square the binomial by using foil • y = 2x2 – 12x + 18 + 4 distribute • y = 2x2 – 12x + 22 combine like terms

  9. Standard Form to Intercept Form • Write the equation in intercept form: • y = – 15x2 + 3x + 12

  10. Standard Form to Intercept Form • Write the equation in intercept form: • y = – 15x2 + 3x + 12 • y = – 3(5x2 – x – 4) common factor

  11. Standard Form to Intercept Form • Write the equation in intercept form: • y = – 15x2 + 3x + 12 • y = – 3(5x2 – x – 4) common factor • y = – 3(5x + 4)(x – 1) factor the trinomial

  12. Standard Form to Vertex Form • Write the equation in vertex form: • y = 3x2 – 6x + 8

  13. Standard Form to Vertex Form • Write the equation in vertex form: • y = 3x2 – 6x + 8 • y = 3(x2 – 2x ) + 8 factor out “a”

  14. Standard Form to Vertex Form • Write the equation in vertex form: • y = 3x2 – 6x + 8 • y = 3(x2 – 2x ) + 8 factor out “a” • y = 3(x2 – 2x + 1) + 8 – 3 complete the square

  15. Standard Form to Vertex Form • Write the equation in vertex form: • y = 3x2 – 6x + 8 • y = 3(x2 – 2x ) + 8 factor out “a” • y = 3(x2 – 2x + 1) + 8 – 3 complete the square • y = 3(x – 1)2 + 5 factor and combine

  16. Vertex Form to Intercept Form • Write the equation in intercept form: • y = (x + 4)2 - 1

  17. Vertex Form to Intercept Form • Write the equation in intercept form: • y = (x + 4)2 - 1 • y = x2 + 8x + 16 - 1 square the binomial by using foil

  18. Vertex Form to Intercept Form • Write the equation in intercept form: • y = (x + 4)2 - 1 • y = x2 + 8x + 16 - 1 square the binomial by using foil • y = x2+ 8x + 15 combine terms

  19. Vertex Form to Intercept Form • Write the equation in intercept form: • y = (x + 4)2 - 1 • y = x2 + 8x + 16 - 1 square the binomial by using foil • y = x2+ 8x + 15 combine terms • y = (x + 3)(x + 5) factor

  20. Intercept Form to Vertex Form • Write the equation in vertex form: • y = (x – 3)(x + 1)

  21. Intercept Form to Vertex Form • Write the equation in vertex form: • y = (x – 3)(x + 1) • y = x2 – 2x - 3 foil

  22. Intercept Form to Vertex Form • Write the equation in vertex form: • y = (x – 3)(x + 1) • y = x2 – 2x - 3 foil • y = x2– 2x - 3 get ready to • y = x2 – 2x + 1 – 3 – 1 complete the square

  23. Intercept Form to Vertex Form • Write the equation in vertex form: • y = (x – 3)(x + 1) • y = x2 – 2x - 3 foil • y = x2 – 2x - 3 get ready to • y = x2 – 2x + 1 – 3 – 1 complete the square • y = (x - 1)2 - 4 factor and combine

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