Respuesta :
Answer:
The correct option is 3.
Step-by-step explanation:
The given equation is
[tex]2x^2+12x-14=0[/tex]
It can be written as
[tex](2x^2+12x)-14=0[/tex]
Taking out the common factor form the parenthesis.
[tex]2(x^2+6x)-14=0[/tex]
If an expression is defined as [tex]x^2+bx[/tex] then we add [tex](\frac{b}{2})^2[/tex] to make it perfect square.
In the above equation b=6.
Add and subtract 3^2 in the parenthesis.
[tex]2(x^2+6x+3^2-3^2)-14=0[/tex]
[tex]2(x^2+6x+3^2)-2(3^2)-14=0[/tex]
[tex]2(x+3)^2-18-14=0[/tex]
[tex]2(x+3)^2-32=0[/tex] .... (1)
Add 32 on both sides.
[tex]2(x+3)^2=32[/tex]
The vertex from of a parabola is
[tex]p(x)=a(x-h)^2+k[/tex] .... (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 [tex]2(x+3)^2=32[/tex] reveals the minimum value for the given equation.
Therefore the correct option is 3.
Answer:
2(x + 3)^2 = 32
Step-by-step explanation:
The "COMPLETING THE SQUARE" lesson makes it clear that this is the correct answer.
(I just took the test)
