Question

The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown. f(x) = 3(x2 – 8x) + 10 = 16 What is the function written in vertex form?

Answer 1

f(x)= 3(x-4)^2 -38 Once you take out the GCF of 3 from the first two terms, then do completing the square.

Answer 2

Answer:  The required vertex form of the given function is

$f(x)=3(x-4)^2-38,$ where the vertex is (4, -38).

Step-by-step explanation:  Given that the first steps in writing $f(x)=3x^2-24x+10$ in vertex form are shown.

$f(x)=3(x^2-8x)+10~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to write the given function in vertex form.

We know that

the vertex form of a function g(x) with vertex at the point (h, k) is given by

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

Therefore, from equation (i), we get

$f(x)=3(x^2-8x)+10\\\\\Rightarrow f(x)=3(x^2-8x+16)-3\times 16+10\\\\\Rightarrow f(x)=3(x-4)^2-48+10\\\\\Rightarrow f(x)=3(x-4)^2-38.$

Thus, the required vertex form of the given function is

$f(x)=3(x-4)^2-38,$ where the vertex is (4, -38).