Question

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

Answer 1

The vertex is at the point;

`(-2,5)`

Step-by-step explanation:

Given the function;

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

Comparing to the quadratic equation;

`y=ax^2+bx+c`

The vertex is at;

`x=(-b)/(2a)`

For the given equation;

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

substituting;

`\begin{gathered} x=-(b)/(2a)=-(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)`