F (x) = (x+3) ^2. Graphing Quadrtic Functions

F (x) = (x + 3) ²

f (x) = (x + 3) (x + 3)

f (x) = x² + 3x + 3x + 9

f (x) = x² + 6x + 9

x² + 6x + 9 = 0

x = - (3) + / - √ ((3) ² - 4 (1) (9))

2 (1)

x = - 3 + / - √ (9 - 36)

2

x = - 3 + / - √ (-27)

2

x = - 3 + / - 3i√ (3)

2

x = - 1.5 + 1.5i√ (3)

f (x) = x² + 6x + 9

f (-1.5 + 1.5i√ (3)) = (-1.5 + 1.5i√ (3)) + 6 (-1.5 + 1.5√ (3)) + 9

f (-1.5 + 1.5i√ (3)) = (2.25 + 3i√ (3) - 6.75) + (-9 + 9√ (3)) + 9

f (-1.5 + 1.5i√ (3)) = (4 + 3i√ (3)) + (-9 + 9√ (3)) + 9

f (-1.5 + 1.5i√ (3)) = 4 - 9 + 9 + 3i√ (3) + 9√ (3)

f (-1.5 + 1.5i√ (3)) = 4 + (3i + 9) √ (3)

(x, f (x)) = (-1.5 + 1.5i√ (3), 4 + (3i + 9) √ (3))

or

f (x) = x² + 6x + 9

f (-1.5 - 1.5i√ (3)) = (-1.5 - 1.5i√ (3)) ² + 6 (-1.5 - 1.5i√ (3)) + 9

f (-1.5 - 1.5i√ (3)) = (2.25 - 3i√ (3) + 6.75) + (-9 - 9i√ (3)) + 9

f (-1.5 - 1.5i√ (3)) = (9 - 3i√ (3)) + (-9 - 9i√ (3)) + 9

f (-1.5 - 1.5i√ (3)) = 9 - 9 + 9 + 3i√ (3) - 9√ (3)

f (-1.5 - 1.5i√ (3)) = 9 + (3i - 9) √ (3)

(x, f (x)) = (-1.5 - 1.5i√ (3), 9 + (3i - 9) √ (3))