Question #d9bde

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Question #d9bde

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Answer 1 · 2017-07-19T01:57:18

$(0, 0) and (- \frac{5}{2}, 0)$ $(0, 0) " " and " " (-5/2, 0)$

Explanation:

The $x$ $x$ intercept of a function occurs when $y = 0$ $y=0$ , since every point on the $x$ $x$ axis has a $y$ $y$ coordinate of $0$ $0$ .

Therefore, to find the $x$ $x$ intercept(s), we need to plug in $0$ $color(red)0$ for $y$ $color(blue)y$ and solve for $x$ $x$ :

$y = 2 x^{2} + 5 x - 3 y$ $color(blue)y = 2x^2 + 5x - 3color(blue)y$

$0 = 2 x^{2} + 5 x - 3 (0)$ $color(red)0 = 2x^2 + 5x - 3(color(red)0)$

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

Notice that you can factor out $x$ $x$ from both terms:

$0 = (x) (2 x + 5)$ $0 = (x)(2x+5)$

Remember that if $a \times b = 0$ $a xx b = 0$ , then either $a = 0$ $a=0$ or $b = 0$ $b=0$ .

$x = 0 or 2 x + 5 = 0$ $x = 0 " " or " " 2x+5 = 0$

$x = 0 or 2 x = - 5$ $x = 0 " " or " " 2x = -5$

$x = 0 or x = - \frac{5}{2}$ $x = 0 " " or " " x = -5/2$

So the $x$ $x$ intercepts are:

$(0, 0) and (- \frac{5}{2}, 0)$ $(0, 0) " " and " " (-5/2, 0)$

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Question #d9bde

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