Mathematics: And ! which of the following reveals the minimum value for the equation 2x2 + 12x − 14 = 0? 2(x + 6)2 = 26 2(x + 6)2 = 20 2(x + 3)2 = 32 2(x + 3)2 = 30

For example, y = k/x; when x = 3 = k = 3y; when y = 9 = k = 27 and x = 27/9 = 3;The answer is 3!...

And ! which of the following reveals the minimum

gobertbrianna40

15.03.2022

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.

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