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

The equation which reveals the minimum value for the equation is  2·x² + 12·x - 14 = 0 is the option;

2·(x + 3)² = 32

Step-by-step explanation:

The given function can be presented as follows;

2·x² + 12·x - 14 = 0

The quadratic equation in standard form is a·(x - h)² + k

Where;

(h, k) is the vertex of the parabola

Given that the coefficient of the x² is positive, the graph is U-shaped and the lowest point is given by the vertex of the graph as follows;

2·x² + 12·x - 14 = 2·x² + 12·x - 14 = 2·(x² + 6·x - 7) = 0

2·(x² + 6·x - 7) = 2·(x² + 6·x + 9 - 7 - 9) = 2·((x + 3)² - 16)

2·((x + 3)² - 16) = 2·(x + 3)² - 32 = 0

∴ 2·x² + 12·x - 14 = 2·(x + 3)² - 32 in vertex form

The minimum value (vertex, (h, k)) for the equation = (-3, -32)

Therefore, the equation which reveals the minimum value for the equation is 2·(x + 3)² = 32

2(x + 3)2 = 32

Step-by-step explanation:

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