# How do you write f(x) = x^2 + 7x + 2 in vertex form?

Apr 23, 2017

In vertex form: $f \left(x\right) = {\left(x + 3.5\right)}^{2} - 10.25$

#### Explanation:

$f \left(x\right) = {x}^{2} + 7 x + 2 \mathmr{and} f \left(x\right) = {\left(x + \frac{7}{2}\right)}^{2} - \frac{49}{4} + 2 \mathmr{and} f \left(x\right) = {\left(x + \frac{7}{2}\right)}^{2} - \frac{41}{4}$

Comparing with standard equation $f \left(x\right) = a {\left(x - h\right)}^{2} + k$, where $\left(h , k\right)$ is vertex.

Vertex is at $\left(- \frac{7}{2} , - \frac{41}{4}\right) \mathmr{and} \left(- 3.5 , - 10.25\right)$

In vertex form: $f \left(x\right) = {\left(x + 3.5\right)}^{2} - 10.25$ [Ans]