Question

PLEASE HELP AND ANSWER!!!!! Which of the following reveals the minimum value for the equation 2x2 + 12x − 14 = 0?

Answer 1

Answer:

The correct option is 3.

Step-by-step explanation:

The given equation is

$2x^2+12x-14=0$

It can be written as

$(2x^2+12x)-14=0$

Taking out the common factor form the parenthesis.

$2(x^2+6x)-14=0$

If an expression is defined as $x^2+bx$ then we add $(\frac{b}{2})^2$ to make it perfect square.

In the above equation b=6.

Add and subtract 3^2 in the parenthesis.

$2(x^2+6x+3^2-3^2)-14=0$

$2(x^2+6x+3^2)-2(3^2)-14=0$

$2(x+3)^2-18-14=0$

$2(x+3)^2-32=0$             .... (1)

Add 32 on both sides.

$2(x+3)^2=32$

The vertex from of a parabola is

$p(x)=a(x-h)^2+k$        .... (2)

If a>0, then k is minimum value at x=h.

From (1) and (2) in is clear that a=2, h=-3 and k=-32. It means the minimum value is -32 at x=-3.

The equation $2(x+3)^2=32$ reveals the minimum value for the given equation.

Therefore the correct option is 3.