Question

question
graph the equation $y = x^2 - 10x + 16$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex. using the graph, determine the equation of the axis of symmetry.
click to plot points. click points to delete them.

Explanation:

Step1: Find the roots (x-intercepts)

Set $y=0$, solve $x^2 -10x +16=0$.
Factor: $(x-2)(x-8)=0$, so $x=2$ and $x=8$.
Points: $(2,0)$ and $(8,0)$

Step2: Find the vertex x-coordinate

Use vertex formula $x=-\frac{b}{2a}$.
For $y=x^2-10x+16$, $a=1$, $b=-10$.
$x=-\frac{-10}{2(1)}=5$

Step3: Find vertex y-coordinate

Substitute $x=5$ into the equation.
$y=(5)^2 -10(5)+16=25-50+16=-9$
Vertex point: $(5,-9)$

Step4: Find 2 additional points

Choose $x=1$: $y=(1)^2-10(1)+16=1-10+16=7$, point $(1,7)$
Choose $x=9$: $y=(9)^2-10(9)+16=81-90+16=7$, point $(9,7)$

Step5: Determine axis of symmetry

Axis of symmetry is the vertical line through vertex x-coordinate.
Equation: $x=5$

Answer:

Plotted points: $(1,7)$, $(2,0)$, $(5,-9)$, $(8,0)$, $(9,7)$
Equation of the axis of symmetry: $x=5$