Let's solve the equation [tex]\( y = ax^2 + c \)[/tex] for [tex]\( x \)[/tex] step by step.
1. Isolate the quadratic term:
[tex]\[
y = ax^2 + c
\][/tex]
Subtract [tex]\( c \)[/tex] from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
y - c = ax^2
\][/tex]
2. Divide by the coefficient of [tex]\( x^2 \)[/tex]:
To solve for [tex]\( x \)[/tex], we need to get rid of the coefficient [tex]\( a \)[/tex]:
[tex]\[
\frac{y - c}{a} = x^2
\][/tex]
3. Take the square root of both sides:
To solve for [tex]\( x \)[/tex], take the positive and negative square roots of both sides:
[tex]\[
x = \pm \sqrt{\frac{y - c}{a}}
\][/tex]
So, the solution to the equation [tex]\( y = ax^2 + c \)[/tex] for [tex]\( x \)[/tex] is:
[tex]\[
x = \pm \sqrt{\frac{y - c}{a}}
\][/tex]
