Solve [tex]\( y = ax^2 + c \)[/tex] for [tex]\( x \)[/tex].

A. [tex]\( x = \pm \sqrt{a y - c} \)[/tex]

B. [tex]\( x = \pm \sqrt{\frac{y - c}{a}} \)[/tex]

C. [tex]\( x = \sqrt{\frac{y}{a} - c} \)[/tex]

D. [tex]\( x = \sqrt{\frac{y + c}{a}} \)[/tex]



Answer :

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]