How do you graph $f(x) = -(x-2)(x + 5)$ ?

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Answer 1 · 2015-07-28T17:40:41

By finding the extremum and the two $x$ -intercepts. And plotting them.

This is a Parabola. And one way to graph Parabolas is to find three strategic points:
$color(red)((1))$ The extremum :

And the extremum occurs when the slope is zero. So, we solve to equation $f'(x)=0$

$=>-(x-2)*1-(x+5)*1=0$

$=>-2x-3=0$

$=>x=-3/2$

Next plug in $x=-3/2$ into $f(x)$ to get the value of $y$

$y=f(3/2)=-(-3/2-2)(-3/2+5)=(7/2)(7/2)=49/4$

So the extremum is $(-3/2,49/4)$

$color(red)((2))$ The roots(the $x$ -intercept) :

We solve the equation $f(x)=0$

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

$=>x=2" "$ and $" "x=-5$

Hence the intercepts are : $(2,0)$ and $" "(-5,0)$

Plot these three points and link them up to obtain a sketch of the graph of $f(x)$ .

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How do you graph f(x) = -(x-2)(x + 5)f(x) = -(x-2)(x + 5)?