1 / 17

Quadratic Functions: Finding Roots and Maximum Height

Learn how to find the roots or zeros of quadratic functions and determine the maximum height of a baseball using quadratic equations.

jackn
Download Presentation

Quadratic Functions: Finding Roots and Maximum Height

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm Ups Saturday, October 19, 2019 Factor each quadratic.

  2. Roots of Quadratic Functions Saturday, October 19, 2019 Essential Question: How do we find the roots or zeros of quadratic functions of the form y = ax2 + bx +c ? Lesson 3.4B

  3. Zeros of a Function Solutions of a quadratic equation or function. • Ify = f(x) is a quadratic function and a is a real number then the following statements are equivalent. • 1. x = a is a zero of f. • 2. x = a is a root of f. • 3. x = a is a solution of the quadratic equation f(x) = 0. • 4. (x – a) is a factor of the quadratic f(x). • 5. (a, 0) is an x-intercept of the graph of y = f(x).

  4. Find the solutions for the quadratic equation. We must set the equation equal to zero before we factor. 1. - 4 +4 -1 +3 The solutions are and .

  5. Find the solutions for the quadratic equation. We must set the equation equal to zero before we factor. 2. +90 +15 +6 +21 The solutions are and .

  6. Find the zeros or roots of the quadratic function. We must substitute zero for “y” and solve the quadratic equation. 3. - 28 +7 -4 +3 The zeros are and .

  7. Find the zeros or roots of the quadratic function. We must substitute zero for “y” and solve the quadratic equation. 4. +36 -12 -3 -15 The roots are and .

  8. Find the x-intercepts of the quadratic function. We must substitute zero for “y” and solve the quadratic equation. 5. +4 +2 +2 +4 If you solve the other equation you will get the same solution. We have only one unique solution! The x-intercept is .

  9. Find the x-intercepts of the quadratic function. We must substitute zero for “y” and solve the quadratic equation. 6. +6 -6 -1 -7 The x-intercepts are and .

  10. Which of the following is the graph of the function f(x) = (x + 3)(x – 3) ? 7. C. A. B.

  11. Find the x-intercepts 8.

  12. Find the zeroes of the function 9.

  13. 10.

  14. Find the maximum value of a quadratic function Baseball 7. The height y(in feet) of a baseball tseconds after it is hit is given by this function: y = –16t2 + 96t + 3 Find the maximum height of the baseball. SOLUTION The maximum height of the baseball is the y-coordinate of the vertex of the parabola with the given equation.

  15. ANSWER The vertex is (3, 147), so the maximum height of the baseball is 147feet. Find the maximum value of a quadratic function y = – 16t2+ 96t +3 Write original function.

  16. Find the maximum value of a quadratic function Suppose the height of the baseball is given by y = – 16t2 + 80t + 2. Find the maximum height of the baseball. 8. SOLUTION The maximum height of the baseball is the y-coordinate of the vertex of the parabola with the given equation. y = – 16t2+ 80t +2 Write original function. The vertex is (2.5, 102), so the maximum height of the baseball is 102feet.

  17. THE END Homework page 81 # 1 – 3 all, 16 – 21 all. 17

More Related