Consider the function f(x) = 4 x^2 + 8x -10 and g(x) = 5x^2 + 10x --1.
Function f is a graph whose vertex is the vertex for the graph of function g. Select the correct answer from the following. Show your work.
a) higher than
b) lower than
c) located at the same axis of symmetry as
The vertex for the graph of function f is the vertex for the graph of function g. Select the correct answer from the following. Show your work.
a) 2 units to the right of
b) 2 units to the left of
c) located at the same axis of symmetry as
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