Question

graph the equation ( y = x^2 - 8x + 15 ) 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 roots (x-intercepts)

Set $y=0$, solve $x^2-8x+15=0$.
Factor: $(x-3)(x-5)=0$, so $x=3$ and $x=5$.
Root points: $(3,0)$ and $(5,0)$

Step2: Calculate vertex x-coordinate

Use formula $x=-\frac{b}{2a}$.
For $y=x^2-8x+15$, $a=1$, $b=-8$.
$x=-\frac{-8}{2\times1}=4$

Step3: Calculate vertex y-coordinate

Substitute $x=4$ into equation.
$y=(4)^2-8(4)+15=16-32+15=-1$
Vertex point: $(4,-1)$

Step4: Find additional points

Choose $x=2$: $y=(2)^2-8(2)+15=4-16+15=3$, point $(2,3)$
Choose $x=6$: $y=(6)^2-8(6)+15=36-48+15=3$, point $(6,3)$

Step5: Identify axis of symmetry

Axis of symmetry is $x=h$ (h from vertex $(h,k)$).
$x=4$

Answer:

Plotted points: $(3,0)$, $(5,0)$, $(4,-1)$, $(2,3)$, $(6,3)$
Equation of axis of symmetry: $x=4$