QUESTION: Graph b.
We are to find the equation of the graph using standard polynomial equation.
Step-by-step explanation:
The graph has three x-intercepts:
x = -3, 2, and 5.
The y intercept is located at (0, 2). At x = -3 and x = 5, the graph passes through the axis linearly, suggesting the corresponding factors of the polynomial will be linear.
At x = 2, the graph bounces off the x-axis at the intercept suggesting the corresponding factor of the polynomial will be second degree (quadratic).
This will now give us:
f(x) = a(x + 3) (x - 2)² (x - 5)
To determine the stretch factor, we determine another point on the graph. We will use the y-intercept (0, -2) to solve for a
f(0) = a(0 + 3) (0 - 2)² (0 - 5)
-2 = a(0 + 3) (0 - 2)² (0 - 5)
-2 = a((3) (-2)² (-5))
-2 = a(3 * 4 * (-5))
-2 = a(12 * -5)
-2 = a(-60)
-2 = -60a
Let's make a subject of formula by dividing both sides by -60
a = -2/-60
a = 1/30
There the graph polynomial appears to represent the function is:
f(x) = 1/30 (x + 3) (x - 2)² (x - 5)