Find vertex and roots of y equals 4x squared plus 6?

y = 4x2 + 6 or

y = 4x2 + 0x + 6, where a = 4, b = 0 and c = 6

x-coordinate of the vertex = -b/2a = -0/2(4) = 0

y-coordinate of the vertex = 4(02) + 6 = 6

vertex is (0, 6)

(Or you can say: Since the vertex of y = x is (0, 0), and this graph is shifted 6 units upward in the y-axis, then the vertex of y = x + 6 would be (0, 0 + 6) or (0, 6)

Substitute 0 for y in order to find the roots.

y = 4x2 + 6

0 = 4x2 + 6

0 - 6 = 4x2 + 6 - 6

-6 = 4x2

-6/4 = 4x2/4

- 6/4 = x2

± √(-6/4) = x

± [√(6/4)]i = x x = [(1/2)√6]i or x = - [(1/2)√6]i