Answer:
Therefore, the solutions of the quadratic equations are:
[tex]x=5,\:x=3[/tex]
The graph is also attached.
Step-by-step explanation:
The solution of the graph could be obtained by finding the x-intercept.
[tex]y=\left(x-\:4\right)^2-1[/tex]
Finding the x-intercept by substituting the value y = 0
so
[tex]y=\left(x-\:4\right)^2-1[/tex]
[tex]\:0\:=\:\left(x\:-\:4\right)^2\:-\:1[/tex] ∵ y = 0
[tex]\left(x-4\right)^2-1=0[/tex]
[tex]\left(x-4\right)^2-1+1=0+1[/tex]
[tex]\left(x-4\right)^2=1[/tex]
[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]\mathrm{Solve\:}\:x-4=\sqrt{1}[/tex]
[tex]\mathrm{Apply\:rule}\:\sqrt{1}=1[/tex]
[tex]x-4=1[/tex]
[tex]x=5[/tex]
[tex]\mathrm{Solve\:}\:x-4=-\sqrt{1}[/tex]
[tex]\mathrm{Apply\:rule}\:\sqrt{1}=1[/tex]
[tex]x-4=-1[/tex]
[tex]x=3[/tex]
So, when y = 0, then x values are 3, and 5.
Therefore, the solutions of the quadratic equations are:
[tex]x=5,\:x=3[/tex]
The graph is also attached. As the graph is a Parabola. It is visible from the graph that the values of y = 0 at x = 5 and x = 3. As the graph is a Parabola.
