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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q 6.101 (page 621)

For the function $f (x) = 2 x^{2} - 7 x + 5$ , find
(a) the zeros of the function
(b) any $x$ -intercepts of the graph of the function
(c) any $y$ -intercepts of the graph of the function.

Short Answer

Expert verified

The zeroes, $x, y$ intercept are $(1, \frac{5}{2}), (1, \frac{5}{2}), 5$ respectively

Step by step solution

01

Given information

Given the function $2 x^{2} - 7 x + 5$

02

Calculate the zeroes

Substituting to zero, we get

$2 x^{2} - 7 x + 5 = 0$

$2 x^{2} - 5 x - 2 x + 5 = 0 x (2 x - 5) - 1 (2 x - 5) = 0 (x - 1) (2 x - 5) = 0 x = 1, \frac{5}{2}$

03

Substitute x=0 for y intercept

Setting to zero, we get

$y = 2 x^{2} - 7 x + 5 y = 2 {(0)}^{2} - 7 (0) + 5 y = 5$

04

Substitute y=0 for x intercept

Setting to zero, we get

$x = 1, \frac{5}{2}$

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Most popular questions from this chapter

Factor $- 7 n + 12 + n^{2}$

In the following exercises, factor completely using the perfect square trinomials pattern.

$36 s^{2} + 84 s + 49$

Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error.

$2 t^{2} + 7 t + 5$

Factor by Grouping In the following exercises, factor by grouping.

$u v - 9 u + 2 v - 18$

Factor Trinomials of the Form $a x^{2} + b x + c$ Using Trial and Error.

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