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

Apr 13, 2018

See below....

Explanation:

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

$\text{ } 5 {x}^{2} - x = 0$
$\Rightarrow \text{ } x \left(5 x - 1 = 0\right)$

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

Also the minimum of the function is at the point where $\frac{\mathrm{dy}}{\mathrm{dx}} = 0$

or,$\text{ } 10 x - 1 = 0$
or,$\text{ } x = 0.1$

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

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