Final answer:
The y-intercept, axis of symmetry, and vertex of the function f(x) = 2x^2 + 4x - 6 are (0, -6), x = -1, and (-1, -8) respectively.
Step-by-step explanation:
The y-intercept represents the point where the graph of a function intersects the y-axis. To find the y-intercept of the given function f(x) = 2x^2 + 4x - 6, set x = 0 and evaluate f(0). Substituting x = 0 into the function gives f(0) = 2(0)^2 + 4(0) - 6 = -6. Therefore, the y-intercept is (0, -6).
The axis of symmetry is a vertical line that divides the parabola into two symmetric halves. The formula for the axis of symmetry is x = -b/(2a), where a and b are the coefficients of x^2 and x in the quadratic equation, respectively. Using the given function f(x) = 2x^2 + 4x - 6, we can identify a = 2 and b = 4. Plugging these values into the formula gives x = -4/(2*2) = -1. Therefore, the axis of symmetry is x = -1.
The vertex is the point on the parabola where the axis of symmetry intersects the curve. To find the vertex, substitute the value of x obtained for the axis of symmetry into the function. Using x = -1 in the function f(x) = 2x^2 + 4x - 6, we get f(-1) = 2(-1)^2 + 4(-1) - 6 = 2 - 4 - 6 = -8. Thus, the vertex is (-1, -8).