To find the vertex of the parabola represented by the equation y = 2x² + 8x + 5, we first note that this is a quadratic equation in the standard form y = ax² + bx + c, where:
- a = 2
- b = 8
- c = 5
The vertex of a parabola in this form can be found using the formula for the x-coordinate of the vertex:
x = -b / (2a)
Substituting the values of a and b into the formula:
x = -8 / (2 * 2) = -8 / 4 = -2
Next, we substitute this x-coordinate back into the original equation to find the y-coordinate of the vertex:
y = 2(-2)² + 8(-2) + 5
Calculating this step by step:
- First, (-2)² = 4, so 2 * 4 = 8
- Then, 8 * (-2) = -16
Now we can combine these values:
y = 8 – 16 + 5 = -3
Thus, the coordinates of the vertex of the parabola are:
(-2, -3)
In conclusion, the vertex of the parabola given by the equation y = 2x² + 8x + 5 is (-2, -3).