Find the vertex f (x) = (x+3) ^2=-4

F (x) = (x + 3) ² = - 4

f (x) = (x + 3) ² + 4

f (x) = ((x + 3) (x + 3)) + 4

f (x) = (x² + 6x + 6x + 9) + 4

f (x) = x² + 12x + 9 + 4

f (x) = x² + 12x + 13

x² + 12x + 13 = 0

x = - 12 + / - √ (12² - 4 (1) (13))

2 (1)

x = - 12 + / - √ (144 - 52)

2

x = - 12 + / - √ (92)

2

x = - 12 + / - 9.59

2

x = - 6 + 4.795

x = - 6 + 4.795 x = - 6 - 4.795

x = - 1.205 x = - 10.795

f (x) = x² + 12x + 13

f (-1.205) = (-1.205) ² + 12 (-1.205) + 13

f (-1.205) = 1.452025 - 14.46 + 13

f (-1.205) = - 13.007975 + 13

f (-1.205) = 0.007975

(x, f (x)) = (-1.205, 0.007975)

or

f (x) = x² + 12x + 13

f (-10.795) = (-10.795) ² + 12 (-10.795) + 13

f (-10.795) = 116.532025 - 129.54 + 13

f (-10.795) = - 13.007975 + 13

f (-10.795) = 0.007975

(x, f (x)) = (-10.795. 0.007975)

vertex: (-1.205, 0.007975) and (-10.795 0.007975)