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Answer 1 · 2017-07-19T01:57:18

$(0, 0) " " and " " (-5/2, 0)$

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

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

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

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

$0 = 2x^2 + 5x$

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

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

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

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

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

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

So the $x$ intercepts are:

$(0, 0) " " and " " (-5/2, 0)$

Final Answer