Question

what is the vertex of y=2(x-3)^2+6 and determine if it’s maximum or minimum value

Answer 1

The general equation of a vertex of a parabola is given by

$\begin{gathered} y=a(x-h)^2+k \\ \text{where} \\ \text{The coordianates of the vertex are} \\ (h,k) \end{gathered}$

If we compare the general equation with that given in question 2

$y=2(x-3)^2+6$

We can infer that

$\begin{gathered} -h=-3 \\ \text{Hence} \\ h=3 \\ \text{Also} \\ k=6 \end{gathered}$

Thus, the vertex is

$(h,k)=(3,6)$

To determine if it is maxima or minima, we will use the graph plot

We can observe that we have a minimum value.

Usually, we can determine this also from the value of a.

If a is negative, we have a maxima

If a is positive, we have a minimum

The value of a =2 (Positive)

Hence, we have a minimum