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 = 2x² + 16x + 17 to vertex form, we complete the square for the x terms.

First, factor out the coefficient of x² from the first two terms:

y = 2(x² + 8x) + 17

To complete the square, we need to add and subtract (8/2)² = 16 inside the parentheses:

y = 2(x² + 8x + 16 - 16) + 17

Simplify the equation:

y = 2[(x + 4)² - 16] + 17

Distribute the 2:

y = 2(x + 4)² - 32 + 17

Simplify the constants:

y = 2(x + 4)² - 15

So, the vertex form of the equation is y = 2(x + 4)² - 15.

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 = 2x² + 16x + 17 to vertex form, we complete the square for the x terms.

First, factor out the coefficient of x² from the first two terms:

y = 2(x² + 8x) + 17

To complete the square, we need to add and subtract (8/2)² = 16 inside the parentheses:

y = 2(x² + 8x + 16 - 16) + 17

Simplify the equation:

y = 2[(x + 4)² - 16] + 17

Distribute the 2:

y = 2(x + 4)² - 32 + 17

Simplify the constants:

y = 2(x + 4)² - 15

So, the vertex form of the equation is y = 2(x + 4)² - 15.

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