Identify the vertex and the axis of symmetry for y = - (x+3) ^2+1

Vertex

y = - (x + 3) ² + 1

y = - (x + 3) (x + 3) + 1

y = - (x² + 3x + 3x + 9) + 1

y = - (x² + 6x + 9) + 1

y = - x² - 6x - 9 + 1

y = - x² - 6x - 8

-x² - 6x - 8 = 0

x = - (-6) + / - √ ((-6) ² - 4 (-1) (-8))

2 (-1)

x = 6 + / - √ (36 - 32)

-2

x = 6 + / - √ (4)

-2

x = 6 + / - 2

-2

x = 6 + 2 x = 6 - 2

-2 - 2

x = 8 x = 4

-2 - 2

x = - 4 x = - 2

y = - x² - 6x - 8

y = - (-4) ² - 6 (-4) - 8

y = - (16) + 24 - 8

y = - 16 + 24 - 8

y = 8 - 8

y = 0

(x, y) = (-4, 0)

or

y = - x² - 6x - 8

y = - (-2) ² - 6 (-2) - 8

y = - (4) + 12 - 8

y = - 4 + 12 - 8

y = 8 - 8

y = 0

(x, y) = (-2, 0)

Axis of Symmetry

The axis of symmetry is equal to - 3.