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.

The standard form of the equation of a parabola is given by y = ax² + bx + c.

Given the standard form of the equation y = x² - 8x + 29, we can complete the square to convert it to vertex form.

First, we group the x terms: y = (x² - 8x) + 29.

Next, we take the coefficient of x, divide it by 2, and square the result to find the value that completes the square. In this case, (-8/2)² = 16.

We add and subtract this value inside the parentheses: y = (x² - 8x + 16 - 16) + 29.

This simplifies to y = ((x - 4)² - 16) + 29.

Finally, we simplify the equation to get it in vertex form: y = (x - 4)² + 13.

So, the vertex form of the equation is y = (x - 4)² + 13, 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.

The standard form of the equation of a parabola is given by y = ax² + bx + c.

Given the standard form of the equation y = x² - 8x + 29, we can complete the square to convert it to vertex form.

First, we group the x terms: y = (x² - 8x) + 29.

Next, we take the coefficient of x, divide it by 2, and square the result to find the value that completes the square. In this case, (-8/2)² = 16.

We add and subtract this value inside the parentheses: y = (x² - 8x + 16 - 16) + 29.

This simplifies to y = ((x - 4)² - 16) + 29.

Finally, we simplify the equation to get it in vertex form: y = (x - 4)² + 13.

So, the vertex form of the equation is y = (x - 4)² + 13, which corresponds to option B.

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