Hello!
Let's look at each one of the questions individually.
The functions f and g have the ( same, different ) axis of symmetry.
An axis of symmetry is the line that goes down the x value of the vertex. It cuts the equation in half, and is the line of symmetry, but for a quadratic.
Looking at function f, we can see where the vertex is by the lowest point, or (-3, -10). This is because the x values have the same interval, and for the numbers before and after (-3, -10), they increase by the same amount. (For example, x = -4 and x = -2 both have y values of -8, and then x = -5 and x = -1 have y values of -2, meaning they are symmetrical)
Function F's axis of symmetry therefore is x = -3, as the x value of the vertex is -3.
Function g's axis of symmetry, we can see from the graph, is x = -3 as well, as drawing an imaginary vertical line through x = -3 bisects the quadratic.
Therefore, the functions f and g have the same axis of symmetry.
The y-intercept of f is ( less than, equal to, greater than ) the y-intercept of g.
The y intercept of an equation is where the equation intersects the y axis. It always has an x value of 0, as x = 0 is the y axis.
Looking at function f, when x = 0, y = 8, meaning the y intercept of function f is y = 8.
Looking at function g, we can see the y value of when the quadratic intercepts the y axis on the graph. It is y = -2.
Therefore, the y-intercept of f is greater than the y-intercept of g.
Over the interval [-6, -3], the average rate of change of f is ( equal to, less than, greater than ) the average rate of change of g.
The rate of change is the amount the y value increases for each x that passes.
For function f, we can see that between x = -6 and x = -3, the function decreases by 18. This means that the overall rate of change is -18 / 3 = -6 (the amount the y changed / difference between x values of points).
For function g, we see that between x = -6 and x = -3, the function increases. In this case, we can't see by exactly how much (as when x = -6, the function doesn't exactly intersect a y value), but we can estimate that it increases by about 9. 9 / 3 = 3.
Therefore, the average rate of change of f is less than the average rate of change of g.
Hope this helped!
