Question

How do you write the quadratic in vertex form given vertex is (-1,-4) and y intercept is 3?

Answer 1

Vertex form: `f(x) = a(x - b/(2a))^2 - 4`. Find a and b.
Standard form: `f(x) = ax^2 + bx + 3.`

`(-b/2a) = -1` -> `a = b/2` -> or b = 2a

`f(-b/2a) = -4 = a - b + 3 = a - 2a + 3` -> a = 7,
and b = 14.

Standard form:`f(x) = 7x^2 + 14x + 3`

Vertex form: `f(x) = 7(x +1)^2 - 4`

Check.
Develop`f(x) = 7(x^2 + 2x + 1) - 4 = 7x^2 + 14x + 3`. Correct