Question

when given y=0.25(x-5)^2+10 what is the value of x?
A) x=5+or- the square root of 4y-10
B) x= 5+or- 2 the square root of y-10
C) X=14+or- the the square root of y-10
D)X=15+or- 2 the square root of y
I did this on my own and got X= 5+or- the square root of y-10 over 0.25 why is this wrong?

Answer 1

Your answer is correct but it is not one of the choices. So it needs to be expressed a little differently. It is like \(\large \frac 14\) vs 0.25. Both mean the same but just different forms.
\[
y=0.25(x-5)^2+10 \\
y - 10 = 0.25(x-5)^2 \\
\frac{y-10}{0.25} = (x-5)^2 \\
\frac{y-10}{\frac 14} = (x-5)^2 \\
4(y-10) = (x-5)^2 \\
\sqrt{4(y-10)} = \sqrt{(x-5)^2} \\
\pm2\sqrt{y-10} = (x-5) \\
x = 5 \pm2\sqrt{y-10}
\]