Find the vertex and the intercepts and then graph the function g x x 2 2 x 2

Find the vertex and the intercepts and then graph the

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Find the vertex and the intercepts, and then graph the function g(x) = x22x 2. EXAMPLE 3Find the vertex and the intercepts, and then graph the function f(x) = 2x2+ 4x 3. . Page 26 of 50 Print | Beginning & Intermediate Algebra 1/31/2014 ...
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PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. The y -intercept is (0, -3). If there are any x -intercepts, they will occur when f(x) = 0. We use the quadratic formula to solve 2 x 2 + 4 x 3 = 0 for x . Because yields an imaginary number, there are no real roots. Thus, there are no x -intercepts for the graph of the function. That is, the graph does not intersect the x -axis. We know that the parabola opens downward . Thus, the vertex is a maximum value at (1, 1). Since this graph has no x -intercepts, we will look for three additional points to help us in drawing the graph. We try f (2), f (3), and f ( 1). Student Practice 3 Find the vertex and the intercepts, and then graph the function g ( x ) = 2 x 2 8 x 6. 583584 9.5 Exercises Find the coordinates of the vertex, the y intercept, and the x intercepts (if any exist) of each of the following quadratic functions. When necessary, approximate the x intercepts to the nearest tenth. 1. f ( x ) = x 2 2 x 8 2. f(x) = x 2 4x 5 3. g ( x ) = x 2 8 x + 9 4. g(x) = x 2 + 4 x + 21 5. p ( x ) = 3 x 2 + 12 x + 3 6. p(x) = 2 x 2 + 4 x + 1 7. r ( x ) = 3 x 2 2 x 6 Page 27 of 50 Print | Beginning & Intermediate Algebra 1/31/2014 ...
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PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. 8. f(x) = 2 x 2 + 3 x 2 9. f ( x ) = 2 x 2 + 2 x 4 10. f ( x ) = 5 x 2 + 2 x 3 In each of the following exercises, find the vertex, the y intercept, and the x intercepts (if any exist), and then graph the function. 11. f(x) = x 2 6 x + 8 12. f ( x ) = x 2 + 6 x +8 13. g ( x ) = x 2 + 2 x 8 14. g ( x ) = x 2 2 x 8 Page 28 of 50 Print | Beginning & Intermediate Algebra 1/31/2014 ...
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PRINTED BY: iicandysi[email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. 584585 15. p ( x ) = x 2 + 8 x 12 16. p ( x ) = x 2 8 x 12 17. r ( x ) = 3 x 2 + 6 x + 4 18. r ( x ) = 3 x 2 +6 x 4 Page 29 of 50 Print | Beginning & Intermediate Algebra 1/31/2014 ...
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PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.
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