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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). If you need a hint …go to next slide to see next step. Intercept Form to Standard Form. Write the equation in standard form:

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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) If you need a hint …go to next slide to see next step.

  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 If you need a hint …go to next slide to see next step.

  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. Intercept Form to Standard Form • Try these: • y = 3(x + 1)(x + 2) • y = ½ (2x + 3)(x – 2) Check your answers on the next slide.

  6. Intercept Form to Standard Form • Try these: • y = 3(x + 1)(x + 2) • y = 3x2 + 9x + 6 • y = ½ (2x + 3)(x – 2) • y = x2– ½ x – 3

  7. Vertex Form to Standard Form • Write this equation in standard form: • y = 2(x – 3)2 + 4 If you need a hint …go to next slide to see next step.

  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 If you need a hint …go to next slide to see next step.

  9. 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 • y = 2x2 – 12x + 18 + 4 distribute If you need a hint …go to next slide to see next step.

  10. 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 • y = 2x2 – 12x + 18 + 4 distribute • y = 2x2 – 12x + 22 combine like terms

  11. Vertex Form to Standard Form • Try these: • y = 3(x + 1)2 – 5 • y = – (x + 3)2 – 2 Check your answers on the next slide.

  12. Vertex Form to Standard Form • Try these: • y = 3(x + 1)2 – 5 • y = 3x2 + 6x – 2 • y = – (x + 3)2 – 2 • y = – x2 – 6x – 11

  13. Standard Form to Intercept Form • Write the equation in intercept form: • y = – 15x2 + 3x + 12 If you need a hint …go to next slide to see next step.

  14. Standard Form to Intercept Form • Write the equation in intercept form: • y = – 15x2 + 3x + 12 • y = – 3(5x2 – x – 4) common factor If you need a hint …go to next slide to see next step.

  15. 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

  16. Standard Form to Intercept Form • Try these: • y = x2 – 12x + 32 • y = 5x2 – 25x + 30 Check your answers on the next slide.

  17. Standard Form to Intercept Form • Try these: • y = x2 – 12x + 32 • y = (x – 8)(x – 4) • y = 5x2 – 25x + 30 • y = 5(x – 2)(x – 3)

  18. Standard Form to Vertex Form • Write the equation in vertex form: • y = 3x2 – 6x + 8 If you need a hint …go to next slide to see next step.

  19. Standard Form to Vertex Form • Write the equation in vertex form: • y = 3x2 – 6x + 8 • y = 3(x2 – 2x ) + 8 factor out “a” If you need a hint …go to next slide to see next step.

  20. 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 If you need a hint …go to next slide to see next step.

  21. 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

  22. Standard Form to Vertex Form • Try these: • y = x2 – 4x + 10 • y = – 2x2 – 4x + 1 Check your answers on the next slide.

  23. Standard Form to Vertex Form • Try these: • y = x2 – 4x + 10 • y = (x – 2)2 + 6 • y = – 2x2 – 4x + 1 • y = – 2(x + 1)2 + 3

  24. More Practice • Write this equation in intercept form: • y = (x + 4)2 – 1 • Write this equation in vertex form: • y = (x – 3)(x + 1) Check your answers on the next slide.

  25. More Practice • Write this equation in intercept form: • y = (x + 4)2 – 1 • y = (x + 5)(x + 3) • Write this equation in vertex form: • y = (x – 3)(x + 1) • y = (x – 1)2 + 1

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