To identify the vertex and the axis of symmetry for the quadratic function given by y = 2x² + 4, we can use the standard form of a quadratic equation, which is represented as y = ax² + bx + c. In our case, a = 2, b = 0, and c = 4.
The vertex of a parabola defined by the equation y = ax² + bx + c can be calculated using the formula:
x = - rac{b}{2a}
Plugging in the values of a and b:
x = - rac{0}{2(2)} = 0
Now, to find the y-coordinate of the vertex, we substitute x = 0 back into the original equation:
y = 2(0)² + 4 = 4
Thus, the vertex of the function is at the point (0, 4).
Next, we determine the axis of symmetry of the parabola, which is a vertical line that runs through the vertex. The equation for the axis of symmetry can be derived from the x-coordinate of the vertex:
x = 0
In conclusion, for the function y = 2x² + 4:
- The vertex is at the point (0, 4).
- The axis of symmetry is represented by the line x = 0.