# How do you graph y=x^2-2x-8?

Jan 2, 2018

Refer explanation.

#### Explanation:

• METHOD 1: ALGEBRA

$y = {x}^{2} - 2 x - 8$ is quadratic in $x$. $a = 1 , b = - 2 , c = - 8$

As coefficient of ${x}^{2}$ is positive so, its graph will be mouth opening upward parabola.

Check discriminant of the quadratic to examine the nature of the roots.
$D = {b}^{2} - 4 a c$
$D = 4 + 32 = 36$
As $D > 0$, the roots of quadratic will be real and unequal. Also, we can find roots of $y = 0$ that are $x = 4 , - 2$

Here, $y = - 8$ at$x = 0$

The minima of the above quadatic is at $x = - \frac{b}{2 a} = \frac{2}{2} = 1$
The value of quadratic at minima $= - \frac{D}{4 a} = - \frac{36}{4} = - 9$

By analysing above all points graph will be
graph{x^2-2x-8 [-25.65, 25.65, -12.83, 12.82]}

• METHOD 2:CALCULUS

Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ and $\frac{{d}^{2} y}{\mathrm{dx}} ^ 2$ . Also check the nature of the graph by derivative tests.