Question

Help with some algebra please?

Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1).

Write the equation of the quadratic function with roots -1 and -7 and a vertex at (-4, 7)

Write the equation of the quadratic function with roots 6 and 10 and a vertex at (8, 2).

Write the equation of the quadratic function with roots 0 and 2 and a vertex at (1, 5).

Answer 1

Vertex form is   f(x) = a(x - b)^2 + c    where the vertex is (b, c) and a is some constant.

So for the first part we have  f(x) = a(x + 6)^2 - 1

for root -9:-  a( -9+6)^2 - 1 = 0
9a - 1 = 0 , a = 1/9

The other 3 are derived in the same way.
so required equation is f(x) = (1/9)(x + 6)^2 - 1