The axis of symmetry and vertex of a quadratic function can be found using its standard form, which is y = ax² + bx + c. In this case, the equation given is y = 2x² + 8x + 3.
To determine the axis of symmetry, we can use the formula:
x = -b / (2a)
Here, a = 2 and b = 8. Plugging these values into the formula:
x = -8 / (2 * 2) = -8 / 4 = -2
So, the axis of symmetry is the vertical line x = -2.
Next, to find the vertex of the parabola, we need to calculate the y-coordinate by substituting x = -2 back into the original equation:
y = 2(-2)² + 8(-2) + 3
y = 2(4) – 16 + 3
y = 8 – 16 + 3 = -5
Therefore, the vertex of the parabola is at the point (-2, -5).
In summary, for the graph of y = 2x² + 8x + 3, the axis of symmetry is x = -2 and the vertex is (-2, -5).