EXAMPLE 5 Change from intercept form to standard

EXAMPLE 6 Change from vertex form to standard form Write f (x) = 4

GUIDED PRACTICE for Examples 5 and 6 Write the quadratic function in standard form.

GUIDED PRACTICE for Examples 5 and 6 10. y = – 4(x – 1)

GUIDED PRACTICE for Examples 5 and 6 12. y = – 7(x – 6)

GUIDED PRACTICE for Examples 5 and 6 13. y = – 3(x + 5)2

GUIDED PRACTICE for Examples 5 and 6 14. g(x) = 6(x - 4)2 –

GUIDED PRACTICE for Examples 5 and 6 15. f(x) = – (x + 2)2

GUIDED PRACTICE for Examples 5 and 6 16. y = 2(x – 3)2 +

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EXAMPLE 5 Change from intercept form to standard form Write y = – 2 (x + 5) (x – 8) in standard form. y= = – 2 (x + 5) (x – 8) – 2 (x 2 – 8 x + 5 x – 40) – 2 (x 2 – 3 x – 40) – 2 x 2 + 6 x + 80 Write original function. Multiply using FOIL. Combine like terms. Distributive property

EXAMPLE 6 Change from vertex form to standard form Write f (x) = 4 (x – 1)2 + 9 in standard form. f (x) = = = 4(x – 1)2 + 9 4(x – 1) + 9 4(x 2 – x + 1) + 9 4(x 2 – 2 x + 1) + 9 4 x 2 – 8 x + 4 + 9 4 x 2 – 8 x + 13 Write original function. Rewrite (x – 1)2. Multiply using FOIL. Combine like terms. Distributive property Combine like terms.

GUIDED PRACTICE for Examples 5 and 6 Write the quadratic function in standard form. 9. y = – (x – 2) (x – 7) y= = – (x – 2) (x – 7) – (x 2 – 7 x – 2 x + 14) – (x 2 – 9 x + 14) – x 2 + 9 x – 14 Write original function. Multiply using FOIL. Combine like terms. Distributive property

GUIDED PRACTICE for Examples 5 and 6 10. y = – 4(x – 1) (x + 3) y= = – 4(x – 1) (x + 3) – 4(x 2 + 3 x – 3) – 4(x 2 + 2 x – 3) – 4 x 2 – 8 x + 12 Write original function. Multiply using FOIL. Combine like terms. Distributive property 11. f(x) = 2(x + 5) (x + 4) = 2(x 2 + 4 x + 5 x + 20) = 2(x 2 + 9 x + 20) = 2 x 2 + 18 x + 40 Write original function. Multiply using FOIL. Combine like terms. Distributive property

GUIDED PRACTICE for Examples 5 and 6 12. y = – 7(x – 6) (x + 1) y= = – 7(x – 6) (x + 1) – 7(x 2 + x – 6) – 7(x 2 – 5 x – 6) – 7 x 2 + 35 x + 42 Write original function. Multiply using FOIL. Combine like terms. Distributive property

GUIDED PRACTICE for Examples 5 and 6 13. y = – 3(x + 5)2 – 1 = – 3(x + 5) – 1 = – 3(x 2 + 5 x + 25) – 1 = – 3(x 2 + 10 x + 25) – 1 = – 3 x 2 – 30 x – 75 – 1 = – 3 x 2 – 30 x – 76 Write original function. Rewrite (x + 5)2. Multiply using FOIL. Combine like terms. Distributive property Combine like terms.

GUIDED PRACTICE for Examples 5 and 6 14. g(x) = 6(x - 4)2 – 10 = 6(x – 4) – 10 = 6(x 2 – 4 x + 16) – 10 = 6(x 2 – 8 x + 16) – 10 = 6 x 2 – 48 x + 96 – 10 = 6 x 2 – 48 x + 86 Write original function. Rewrite (x – 4)2. Multiply using FOIL. Combine like terms. Distributive property Combine like terms.

GUIDED PRACTICE for Examples 5 and 6 15. f(x) = – (x + 2)2 + 4 = – (x + 2) + 4 = – (x 2 + 2 x + 4) + 4 = – (x 2 + 4 x + 4) + 4 = – x 2 – 4 x – 4 + 4 = – x 2 – 4 x Write original function. Rewrite (x + 2)2. Multiply using FOIL. Combine like terms. Distributive property Combine like terms.

GUIDED PRACTICE for Examples 5 and 6 16. y = 2(x – 3)2 + 9 = 2(x – 3) + 9 = 2(x 2 – 3 x + 9) + 9 = 2(x 2 – 6 x + 9) + 9 = 2 x 2 – 12 x + 18 + 9 = 2 x 2 – 12 x + 27 Write original function. Rewrite (x – 3)2. Multiply using FOIL. Combine like terms. Distributive property Combine like terms.