Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Use the function f(x) = 4x² - 7x-15 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph

Sagot :

xero099

a) The factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).

b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).

c) The function has a minimum and grows in the + y direction.

d) Marking the two x-intercepts, second, generating a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and estimate the location of the vertex and, finally, creating a parabola with a minimum and growing in the + y direction by matching the points.

How to analyze and interpret quadratic functions?

In this problem we have a quadratic function in standard form, that is, an equation of the form f(x) = a · x² + b · x + c, where a, b and c are real coefficients. a) First, we need to complete the square and find the roots to determine the factorized form:

4 · x² - 7 · x - 15 = 0

4 · [x² - (7 / 4) · x - (15 / 4)] = 0

x² - (7 / 4) · x - (15 / 4) = 0

x² - 2 · (7 / 8) · x - (15 / 4) + (289 / 64) = 289 / 64

x² - 2 · (7 / 8) · x + 49 / 64 = 289 / 64

(x - 7 / 8)² = 289 / 64

x - 7 / 8 = ± 17 / 8

x = 7 / 8 ± 17 / 8

Then, the factor form of the polynomial is f(x) = 4 · (x - 3) · (x + 5 / 4).

b) The values of the x-intercepts of the graph of f(x) are represented by the roots found in part a).

c) The end behavior of the graph is inferred from the lead coefficient. A positive coeffcient , which is the case of the function, indicates that vertex of the polynomial is a minimum and parabola grows in the + y direction.

d) In accordance with algebra, we can generate a quadratic equation by knowing three distinct points on Cartesian plane.

First, mark the two x-intercepts, second, generate a line perpendicular to the x-axis that passes the midpoint of the line segment generated by the two intercepts and, finally, generate a parabola with a minimum and growing in the + y direction.

To learn more on quadratic equations: https://brainly.com/question/17177510

#SPJ1

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.