Question

Solve the following quadratic function by utilizing the square root method. y = x2 - 64​

Answer 1

Answer:

$x=\pm\sqrt{y+64}$

Step-by-step explanation:

All you need to do is isolate the x.

First, add 64 to both sides:

$y=x^2-64\\x^2-64+64=y+64\\x^2=y+64$

Then, take the square root of both sides:

$\sqrt{x^2}=\sqrt{y+64}\\x=\sqrt{y+64$

Actually, that is:

$x=\pm\sqrt{y+64}$

Here's the reason for that. An example would be:

$x^2=4$

Here, you'd take the square root of both sides to solve for x.

$\sqrt{x^2}=\sqrt{4}\\x=2$

Right? But X could also be a -2, because a negative times a negative is a positive.

$(-2)^2=4\\-2\times-2=4\\4=4$

Therefore, $x=2, -2$ or $x=\pm2$

$x^2=2\times2=4\\x^2=-2\times-2=4$