Page 153 - Algebra

Explanation:
The graph crosses the x-axis. Therefore, the polynomial has an odd number of roots.
The graph shows three places of intersections at A, B, and C. It's a three-degree polynomial.
Therefore, the roots are: -2, -1,and 1
1.
2.
3. At a point where the graph changes from increasing to decreasing, the function has a local maximum value.
Here, the graph changes from increasing to decreasing at x = 2. So, the function has a maximum value at x = 2.
4. From the graph, it’s clear that f(6) = –4
5.
6. The minimum value of the function is at x = –2; the value is – 3.
When a function has an intercept at a, (x – a) is a factor of the polynomial. Therefore, the
function is
f(x) = (x + 4)(x + 2)(x – 4)(x –2)
f(x) = (x2 – 16)(x2 – 4)
The function increases from –2 ≤ x ≤ 2 and 5 ≤ x ≤ 7. Therefore, at 2 points, the function
increases.
Page 152 of 177
Algebra I & II