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 $x=1$ or $x=5$. Roots: $(1,0)$ and $(5,0)$.

Step2: Find vertex x-coordinate

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

Step3: Find vertex y-coordinate

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

Step4: Find 2 additional points

Choose $x=0$: $y=0^2-6(0)+5=5$, point $(0,5)$.
Choose $x=6$: $y=6^2-6(6)+5=36-36+5=5$, point $(6,5)$.

Answer:

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