Question

What is the vertex of Y=x^2+4x+9

Answer 1

Answer:

The vertex is at the point;

$(-2,5)$

Explanation:

Given the function;

$y=x^2+4x+9$

Comparing to the quadratic equation;

$y=ax^2+bx+c$

The vertex is at;

$x=\frac{-b}{2a}$

For the given equation;

$\begin{gathered} a=1 \\ b=4 \end{gathered}$

substituting;

$\begin{gathered} x=-\frac{b}{2a}=-\frac{4}{2(1)} \\ x=-2 \end{gathered}$

The value of y at x=-2 is;

$\begin{gathered} y=x^2+4x+9 \\ y=(-2)^2+4(-2)+9 \\ y=4-8+9 \\ y=5 \end{gathered}$

Therefore, the vertex is at the point;

$(-2,5)$