Consider the functions f(x)=4x^2+8x-10 and g(x)=55x^2+20x-1
Function f is a graph whose vertex is
higher than
lower than
located at the same axis of symmetry as the vertex for the graph of function g
The vertex of a quadratic function in the form of f(x)=ax^2+bx+c is given by the coordinates (-b/2a, f(-b/2a)).
For f(x)=4x^2+8x-10, the vertex is located at (-8/(2*4), f(-8/(2*4))) = (-1, 4(-1)^2+8(-1)-10) = (-1, -2).
For g(x)=55x^2+20x-1, the vertex is located at (-20/(2*55), g(-20/(2*55))) = (-20/110, 55(-20/110)^2+20(-20/110)-1) = (-20/110, 55/121 - 40/11 -1) = (-20/110, -11/121).
Comparing the y-coordinates of the two vertices, we see that the vertex for f(x) is lower than the vertex for g(x) since -2 < -11/121.
Therefore, the vertex for the graph of function f is lower than the vertex for the graph of function g.