# What are the important points needed to graph y=x^2- 6x+2?

Apr 14, 2016

$y = {x}^{2} - 6 x + 2$ represents a parabola. Axis of symmetry is x = 3. Vertex is $V \left(3 , - 7\right)$. Parameter $a = \frac{1}{4}$. Focus is $S \left(3 , - \frac{27}{4}\right)$. Cuts x-axis at $\left(3 \pm \sqrt{7} , 0\right)$. Directrix equation: $y = - \frac{29}{4}$. .

#### Explanation:

Standardize the form to $y + 7 = {\left(x - 3\right)}^{2}$.
Parameter a is given 4a = coefficient of ${x}^{2}$ = 1.
Vertex is $V \left(3 , - 7\right)$.
The parabola cuts x-axis y = 0 at $\left(3 \pm \sqrt{7} , 0\right)$.
The axis of symmetry is x = 3, parallel to y-axis, in the positive direction, from the vertex

Focus is S(3, -7-1.4)#, on the axis x = 3, at a distance a =1/4, above the focus.

Directrix is perpendicular to the axis, below the vertex, at a distance a = 1/4, V bisects the altitude from S on the directrix.