How do you find the vertex of the parabola given by the equation y = 2x² + 8x + 5?

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Finding the Vertex of a Parabola

The vertex of a parabola described by the quadratic equation in the form of y = ax² + bx + c can be found using the vertex formula:

x

Step-by-Step Calculation

Given the equation:

y = 2x² + 8x + 5

Here, we identify:

  • a = 2
  • b = 8
  • c = 5

Calculate the x-coordinate:

Using the formula:

x = -b / (2a)

Plugging in the values:

x = -8 / (2 * 2) = -8 / 4 = -2

Calculate the y-coordinate:

Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x back into the original equation:

y = 2(-2)² + 8(-2) + 5

Calculating this:

  • 2 * 4 = 8
  • 8 * -2 = -16

Therefore:

y = 8 – 16 + 5 = -3

Conclusion

The coordinates of the vertex are:

(-2, -3)

This means that the vertex of the parabola given by the equation y = 2x² + 8x + 5 is at the point (-2, -3).

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