Question

Find the vertex of the graph of the quadratic function by completing the square or using the vertex formula. f(x) = 3x2 - 18x+4

Answer 1

Given:

$f(x)=3x^2-18x+4$

Using the vertex form:

$f(x)=a(x-h)^2+k$

We have:

$f(x)=3(x^2-6x)+4$$f(x)=3\lbrack(x-3)^2-9\rbrack+4$

We know that h = 3

and K = f(h) = f(3)

Thus, we have:

$\begin{gathered} f(3)=3(3)^2-18(3)\text{ + 4 } \\ \text{ = 27-54+4} \\ \text{ = }-23 \end{gathered}$

Therefore, the vertex form of the equation is:

$f(x)\text{ = 3(}x-3)^2-23$

ANSWER:

$f(x)\text{ = 3(}x-3)^2-23$