Question

Use the following information about the graph of a polynomial function to determine the formula for the function. • The $y$-intercept is (0, 160). • The $x$-intercepts are (2, 0), (5, 0), (-2, 0), and (-4, 0). • Degree is 4. • End behavior: $f(x) \to \infty$ as $x \to -\infty$, and $f(x) \to \infty$ as $x \to \infty$. f(x) =

          Use the following information about the graph of a polynomial function to determine the formula for the function.
• The $y$-intercept is (0, 160).
• The $x$-intercepts are (2, 0), (5, 0), (-2, 0), and (-4, 0).
• Degree is 4.
• End behavior: $f(x) \to \infty$ as $x \to -\infty$, and $f(x) \to \infty$ as $x \to \infty$.
f(x) =

Show more…

Use the following information about the graph of a polynomial function to determine the formula for the function.
• The y-intercept is (0, 160).
• The x-intercepts are (2, 0), (5, 0), (-2, 0), and (-4, 0).
• Degree is 4.
• End behavior: f(x) →∞ as x → -∞, and f(x) →∞ as x →∞.
f(x) =

Added by Jacob L.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Julie Silva

05/19/2022

Step 1

Step 1: Factor out the common term x^2 from each term in the function. Show more…

Show all steps

lock

Thanks for your feedback!

f(x) = x^4 - 2050x^3 + 40000x^2

Play audio

Feedback

Powered by NumerAI

Julie Silva and 68 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 The finding equation to represent the graph shown here in the diagram.

00:05 So the first thing you want to do is you want to find the zeros for the function.

00:08 Remember, the zeros represent where the graph hits or crosses the x -axis.

00:12 Well, it looks like it hits when x is equal to negative 2, as well as when x is equal to positive 1.

00:18 So we have two zeros in this case.

00:20 Now, the second thing that we want to do is we want to find each of our zeros multiplicity.

00:25 Now, the multiplicity of a zero tells us if the graph just hits, the x -axis and turns around, or if it goes through the x -axis.

00:34 So notice, when x is negative 2, the graph hits the x -axis, but then it turns back down.

00:39 It doesn't go through, which means that this 0 will have an even multiplicity.

00:43 So i'll put a multiplicity of 2 here.

00:45 Now, when x is equal to 1, notice that the graph goes through the x -axis, which means it has an odd multiplicity, so i'll put a 1 here.

00:53 Okay, so now that we have our multiplicities and our 0s, we can go ahead and find our factors.

00:59 So remember, to find our factors, we use the opposite sign.

01:02 In other words, because x equals negative 2 is a 0, we know that x plus 2 is a factor.

01:07 And because 1 is a 0, then x minus 1 is a factor...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later