Question

Solve 0 = (x – 4)2 – 1 by graphing the related function.

What are the solutions to the equation?

3 and 5 is the answer
AND THAT'S JUST ON PERIOD POOH!

Answer 1

3 and 5 is the answer

Explanation:

Answer 2

Therefore, the solutions of the quadratic equations are:

`x=5,\:x=3`

The graph is also attached.

Explanation:

The solution of the graph could be obtained by finding the x-intercept.

`y=\left(x-\:4\right)^2-1`

Finding the x-intercept by substituting the value y = 0

so

`y=\left(x-\:4\right)^2-1`

`\:0\:=\:\left(x\:-\:4\right)^2\:-\:1` ∵ y = 0

`\left(x-4\right)^2-1=0`

`\left(x-4\right)^2-1+1=0+1`

`\left(x-4\right)^2=1`

`\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=√(f\left(a\right)),\:\:-√(f\left(a\right))`

`\mathrm{Solve\:}\:x-4=√(1)`

`\mathrm{Apply\:rule}\:√(1)=1`

`x-4=1`

`x=5`

`\mathrm{Solve\:}\:x-4=-√(1)`

`\mathrm{Apply\:rule}\:√(1)=1`

`x-4=-1`

`x=3`

So, when y = 0, then x values are 3, and 5.

Therefore, the solutions of the quadratic equations are:

`x=5,\:x=3`

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.