The vertex form of a parabola's equation is given by y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

To convert the standard form y = ax² + bx + c to the vertex form, we can complete the square for the x terms.

Given the standard form of the equation of the parabola y = 7x² + 14x + 4, we can rewrite the x terms as follows:

y = 7(x² + 2x) + 4

To complete the square, we take half of the coefficient of x, square it, and add and subtract it inside the parenthesis:

y = 7[(x² + 2x + 1) - 1] + 4

Simplify the equation:

y = 7[(x + 1)² - 1] + 4

y = 7(x + 1)² - 7 + 4

y = 7(x + 1)² - 3

So, the vertex form of the equation is y = 7(x + 1)² - 3, which corresponds to option B.

Question

The vertex form of a parabola's equation is given by y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

To convert the standard form y = ax² + bx + c to the vertex form, we can complete the square for the x terms.

Given the standard form of the equation of the parabola y = 7x² + 14x + 4, we can rewrite the x terms as follows:

y = 7(x² + 2x) + 4

To complete the square, we take half of the coefficient of x, square it, and add and subtract it inside the parenthesis:

y = 7[(x² + 2x + 1) - 1] + 4

Simplify the equation:

y = 7[(x + 1)² - 1] + 4

y = 7(x + 1)² - 7 + 4

y = 7(x + 1)² - 3

So, the vertex form of the equation is y = 7(x + 1)² - 3, which corresponds to option B.

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