Given the function h(x) = x² - 7x - 8. The extremum of the function is the minimum one and its value is h(x) = -32.5
The relation between symmetry of the graph and the extremum point is:
Suppose x = p is the line equation of the graph's symmetry, then f(p) is the extremum value.
The given function is:
h(x) = x² - 7x - 8
Find the x-intercepts:
h(x) = 0
x² - 7x - 8 = 0
(x + 1) (x - 8) = 0
x = -1 or x = 8
The symmetry lies in the middle of x-intercepts. Hence, the symmetry occurs at:
x = (-1 + 8) / 2
x = 3.5
The extremum point is:
h(3.5) = 3.5² - 7 x 3.5 - 8 = -32.5
Since the quadratic term x² has a positive coefficient, the graph is open downward, hence the extremum point is the minimum one.
Complete question:
Find the extremum of each function using the symmetry of its graph. classify the extremum of the function as a maximum or a minimum and state the value of x at which it occurs. h(x) = x² - 7x - 8
Learn more about extremum value here:
https://brainly.com/question/29500135
#SPJ4
