Question

Complete the square of the following function:
f(x) = 3x² - 12x + 6
1) (2, -6)
2) (-2, -6)
3) 2, 6)
4) -6, 2)

Answer 1

Answer:

The option 1) i.e. (2, -6) is true.

Step-by-step explanation:

Considering the function

$f(x) = 3x^{2} - 12x + 6$

$\mathrm{Write}\:3x^2-12x+6\:\mathrm{in\:the\:form:\:\:}x^2+2ax+a^2$

= $3x^{2} -12x+6$

$\mathrm{Factor\:out\:}3$

= $3(x^{2} -4x)+6$

Completing the square:

$=3\left(x^2-4x+2+\left(-2\right)^2-\left(-2\right)^2\right)$

As

$x^2+2ax+a^2=\left(x+a\right)^2$

$x^2-4x+\left(-2\right)^2=\left(x-2\right)^2$

$\mathrm{Complete\:the\:square}$

$=3\left(\left(x-2\right)^2+2-\left(-2\right)^2\right)$

$=3\left(x-2\right)^2-6$

The vertex form of a quadratic function  $f(x) = a(x-h)^{2} + k$, where (h, k) be the vertex of the parabola.

The vertex form of the equation is: $f(x)=3\left(x-2\right)^2-6$

If we may compare this equation with the general vertex form, we will find that h = 2 and k = -6, so the vertex is at (2, -6).

Therefore, option 1) i.e. (2, -6) is true.

Keywords: completing the square, function

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