How do you identify the important parts of $y = 5 x^{2} - x$ $y= 5x^2-x$ to graph it?

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Answer 1 · 2018-04-13T05:29:01

See below....

The $x$ $x$ -intercepts can be found out by putting $y = 0$ $y=0$ in the equation.

$5 x^{2} - x = 0$ $" "5x^2-x=0$
$\Rightarrow x (5 x - 1 = 0)$ $rArr" "x(5x-1=0)$

So $x = 0$ $x=0$ and $x = \frac{1}{5} = 0.2$ $x=1/5=0.2$

Also the minimum of the function is at the point where $\frac{d y}{d x} = 0$ $dy/dx=0$

or, $10 x - 1 = 0$ $" "10x-1=0$
or, $x = 0.1$ $" "x=0.1$

The function is a parabola of the form $x^{2} = 4 a y$ $x^2=4ay$ and $y = + \infty$ $y=+oo$ when $x \to \pm \infty$ $x->+-oo$ .

graph{5x^2-x [-1.108, 1.292, -0.239, 0.96]}

How do you identify the important parts of y=5x2−xy= 5x^2-x to graph it?