Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.5 $x^{3}$ - 1.7 $x^{2}$ + 2.3x - 2; $g(x)$ = 2.8x - 4.8
A) (-1.21519, -3.40253)
(1)46104, 8.83163)
(3)15415, 4.0909)
B) (-1.21519, -8.20253),
(3)15415, 4.03163)
C) (-1.21519, -8.20253),
(1)46104, -0.7091)
(3)15415, 4.03163)
D) (-1.21519, -3.40253)
(3)15415, 4.0909)

Question

Quizplus · Accepted Answer

To find the points of intersection, we need to solve the equation f(x) = g(x). This gives us the equation 0.5$x^{3}$ - 1.7$x^{2}$ + 2.3x - 2 = 2.8x - 4.8. Simplifying, we get the cubic equation 0.5$x^{3}$ - 1.7$x^{2}$ - 0.5x + 2 = 0. Using a graphing calculator or software, we can see that this equation has three real roots. Using a numerical method such as Newton's method, we can approximate these roots as:

- x ≈ -1.21519, y ≈ -8.20253
- x ≈ 1.46104, y ≈ 8.83163
- x ≈ 3.15415, y ≈ 4.0909

Therefore, the points of intersection are approximately (-1.21519, -8.20253), (1.46104, 8.83163), and (3.15415, 4.0909). The only choice that includes all three of these points is choice C.

Find the Points of Intersection of the Graphs of the Functions