To compare the heights of the vertex for f(x) and g(x), we need to write both functions in vertex form.
For f(x) = 4x^2 + 8x - 10, we complete the square:
f(x) = 4(x^2 + 2x) - 10
f(x) = 4(x^2 + 2x + 1) - 4 - 10
f(x) = 4(x + 1)^2 - 14
The vertex for f(x) is (-1, -14).
For g(x) = 5x^2 + 10x - 1, we complete the square:
g(x) = 5(x^2 + 2x) - 1
g(x) = 5(x^2 + 2x + 1) - 5 - 1
g(x) = 5(x + 1)^2 - 6
The vertex for g(x) is (-1, -6).
Comparing the heights of the vertices, we see that the vertex of f(x) is lower than the vertex of g(x). Therefore, the correct answer is:
b) lower than
To determine the relationship between the axes of symmetry for f(x) and g(x), we observe that the axis of symmetry for a parabola in vertex form y = a(x - h)^2 + k is x = h.
Since the vertex for both f(x) and g(x) is at x = -1, we can conclude that:
c) located at the same axis of symmetry as