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How can I find equations for these graphs using the standard polynomial equation?

How can I find equations for these graphs using the standard polynomial equation?-example-1
User Gary Liu
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1 Answer

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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)

User Mayur Vaghasiya
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2.8k points
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