Question

graph the equation $y = x^2 - 6x + 5$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex. using the graph, determine the vertex of the parabola.
click to plot points. click points to delete them.

Explanation:

Step1: Find roots (y=0)

Set $y=0$, solve $x^2-6x+5=0$.
Factor: $(x-1)(x-5)=0$, so $x=1, x=5$.
Points: $(1,0), (5,0)$

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$ for $ax^2+bx+c$.
$x=-\frac{-6}{2(1)}=3$

Step3: Find vertex y-coordinate

Substitute $x=3$ into equation:
$y=(3)^2-6(3)+5=9-18+5=-4$
Vertex: $(3,-4)$

Step4: Find 2 extra points

Choose $x=0$: $y=0-0+5=5$, point $(0,5)$
Choose $x=6$: $y=36-36+5=5$, point $(6,5)$

Step5: Verify 5 points

Points: $(0,5), (1,0), (3,-4), (5,0), (6,5)$

Answer:

The vertex of the parabola is $\boldsymbol{(3, -4)}$
The 5 points to plot are: $(0,5)$, $(1,0)$, $(3,-4)$, $(5,0)$, $(6,5)$