Question

put the quadratic into vertex form and state the coordinates of the vertexy=x2+6x+13

Answer 1

Quadratic function: Vertex form is represented by:

$\begin{gathered} f(x)=a(x-h)^2+k \\ \text{where (h, k) is the vertex} \end{gathered}$

Standard form is:

$\begin{gathered} f(x)=ax^2+bx+c \\ y=x^2+6x+13 \end{gathered}$

To get the vertex of the quadratic graph, we can use the following formulas:

$\begin{gathered} h=-\frac{b}{2a} \\ k=f(h) \end{gathered}$

Then, calculating h:

$\begin{gathered} h=-\frac{6}{2(1)} \\ h=-\frac{6}{2}=-3 \end{gathered}$

k, would be f(-3):

$\begin{gathered} k=(-3)^2+6(-3)+13 \\ k=9-18+13 \\ k=4 \end{gathered}$

Therefore, the quadratic function in vertex form would be:

$y=(x+3)^2+4$

Coordinates of the vertex (-3, 4).