Write the standard form equation of a parabola given the following root and point on the graph. root: −3 + 𝑖; point (−2,4)

Answer 1

well then -3 - i is also a root

So f(-3 + i) = 0

f(-3 - i) = 0

and f(-2) = 4

f(x) = k[(x+3) - i ][ (x+3) + i]

= k[ (x+3)^2 - -1]

= k [ x^2 + 6x + 9 + 1]

=k [ x^2 + 6x + 10]

Finally

4 = k [ (-2)^2 + 6(2) + 10 ]

4 = k [ 4 + 12 + 10]

4 = k[ 26]

4/26 = k

k = 2/13

f(x) = (2/13)(x^2 + 6x + 10)