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 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 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 distribute
y = 2x2 – 12x 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) 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