4.2B – “FOIL”

1. 4.2B – “FOIL” • Used to turn VERTEX form or INTERCEPT (factored) form into STANDARD form. • Multiply 2 factors (binomials : 2 terms with + or -) • ( F L) (F L) F = First terms in each parenthesis (multiply) O = Outside terms (multiply) I = Inside terms (multiply) L = Last terms in each parenthesis (multiply) Combine (add) “O” and “I” terms (alike) Put result in STANDARD form: y= ax² + bx + c

2. Examples: Multiply the binomials (FOIL) • 1. (x + 4)(x + 7) • 2. (x – 3) (x + 2) • 3. (x + 5) (x – 2) • 4. (x – 2 ) (x – 4 )

3. Turn Intercept (factored) form into Standard Form • INTERCEPT form: y = a(x – p) (x – q) • 1. “FOIL” the 2 factors (x – p) (x – q) • 2. Put result (trinomial) in a parenthesis • 3. Distribute “a” to the trinomial • 4. Put terms in STANDARD form:y=ax² + bx + c

4. Examples: Put into Standard Form • 5. y = -2(x + 5)(x – 8) • 6. y = 2(x + 5)(x + 4) • 7. y = -7(x – 6 )(x + 1) • 8. y = - (x – 2 )(x – 7 )

5. Turn Vertex Form into Standard • Vertex Form y = a(x- h )² + k 1. Write the (x – h) TWICE 2. FOIL the 2 factors 3. Put result (Trinomial) inside parenthesis 4. Distribute “a” to the trinomial 5. Combine like terms ( new c and K ) 6. Put terms in standard form: y = ax² + bx + c

6. Examples: Put into Standard Form • 9. 4(x – 1 )² + 9 • 10. -3(x + 5)² - 1 • 11. 2(x – 3)² + 9 • 12. -(x + 2)² + 4