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

1 Answer
May 16, 2015

Vertex form: f(x) = a(x - b/(2a))^2 - 4f(x)=a(xb2a)24. Find a and b.
Standard form: f(x) = ax^2 + bx + 3.f(x)=ax2+bx+3.

(-b/2a) = -1 (b2a)=1 -> a = b/2a=b2 -> or b = 2a

f(-b/2a) = -4 = a - b + 3 = a - 2a + 3 f(b2a)=4=ab+3=a2a+3 -> a = 7,
and b = 14.

Standard form: f(x) = 7x^2 + 14x + 3f(x)=7x2+14x+3

Vertex form: f(x) = 7(x +1)^2 - 4f(x)=7(x+1)24

Check.
Develop f(x) = 7(x^2 + 2x + 1) - 4 = 7x^2 + 14x + 3f(x)=7(x2+2x+1)4=7x2+14x+3. Correct