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

May 16, 2015

Vertex form: $f \left(x\right) = a {\left(x - \frac{b}{2 a}\right)}^{2} - 4$. Find a and b.
Standard form: $f \left(x\right) = a {x}^{2} + b x + 3.$

$\left(- \frac{b}{2} a\right) = - 1$ -> $a = \frac{b}{2}$ -> or b = 2a

$f \left(- \frac{b}{2} a\right) = - 4 = a - b + 3 = a - 2 a + 3$ -> a = 7,
and b = 14.

Standard form:$f \left(x\right) = 7 {x}^{2} + 14 x + 3$

Vertex form: $f \left(x\right) = 7 {\left(x + 1\right)}^{2} - 4$

Check.
Develop$f \left(x\right) = 7 \left({x}^{2} + 2 x + 1\right) - 4 = 7 {x}^{2} + 14 x + 3$. Correct