graph the equation $y = x^2 - 14x + 48$ on the accompanying set of axes. you must plot 5 points including…

graph the equation $y = x^2 - 14x + 48$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex.\nclick to plot points. click points to delete them.

graph the equation $y = x^2 - 14x + 48$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex.\nclick to plot points. click points to delete them.

Answer

Explanation:

Step1: Find roots (y=0)

Set $y=0$, solve $x^2-14x+48=0$. Factor: $(x-6)(x-8)=0$. So $x=6$ and $x=8$. Roots: $(6,0)$ and $(8,0)$.

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$. For $ax^2+bx+c$, $a=1$, $b=-14$. $x=-\frac{-14}{2(1)}=7$

Step3: Find vertex y-coordinate

Substitute $x=7$ into equation: $y=(7)^2-14(7)+48=49-98+48=-1$. Vertex: $(7,-1)$.

Step4: Find additional points

Choose $x=5$: $y=5^2-14(5)+48=25-70+48=3$. Point: $(5,3)$. Choose $x=9$: $y=9^2-14(9)+48=81-126+48=3$. Point: $(9,3)$.

Answer:

The 5 points to plot are: $(5, 3)$, $(6, 0)$, $(7, -1)$, $(8, 0)$, $(9, 3)$ (Plot these points on the axes and draw a smooth parabola through them.)