Consider h (x) = - x2 + 8x + 15. Identify its vertex and y-intercept.

H (x) = - x² + 8x + 15

Vertex: h (x) = - x² + 8x + 15

y = - x² + 8x + 15

y - 15 = - x² + 8x

y - 15 = - 1 (x²) - 1 (8x)

y - 15 = - 1 (x² - 8x)

y - 15 - 1 (16) = - 1 (x² - 8x + 16)

y - 15 - 16 = - 1 (x² - 4x - 4x + 16)

y - 31 = - 1 (x (x) - x (4) - 4 (x) - 4 (4))

y - 31 = - 1 (x (x - 4) - 4 (x - 4))

y - 31 = - 1 (x - 4) (x - 4)

y - 31 = - 1 (x - 4) ²

y - 31 + 31 = - 1 (x - 4) ² + 31

y = - 1 (x - 4) ² + 31

y = - 1 (x + (-4)) ² - (-31)

h (x) = - 1 (x + (-4)) ² - (-31)

(h, k) = (4, 31)

Y-Intercept: h (x) = - x² + 8x + 15

y = - x² + 8x + 15

y = - (0) ² + 8 (0) + 15

y = - (0) + 0 + 15

y = - 0 + 0 + 15

y = 0 + 15

y = 15

h (x) = 15

(x, y) = (0, 15)