Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To solve the equation \( y = a x^2 + c \) for \( x \), we need to isolate \( x \) step-by-step. Let's go through the process:
1. Start with the given equation:
[tex]\[ y = a x^2 + c \][/tex]
2. Isolate the \( x^2 \) term:
[tex]\[ y - c = a x^2 \][/tex]
3. Divide both sides by \( a \):
[tex]\[ \frac{y - c}{a} = x^2 \][/tex]
4. Take the square root of both sides to solve for \( x \):
Since taking the square root can result in both positive and negative roots, we get:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
So, the correctly solved equation for \( x \) is:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
Let's cross-check the provided options:
- \( x = \pm \sqrt{a y - c} \): This is not correct because it suggests multiplication inside the square root in a form not derived from the equation.
- \( x = \pm \sqrt{\frac{y - c}{a}} \): This is indeed the correct solution.
- \( x = \sqrt{\frac{y}{a} - c} \): This is wrong because the term \( c \) should be adjusted for multiplication/division prior to isolating \( x \).
- \( x = \sqrt{\frac{y + c}{a}} \): This is incorrect since subtracting \( c \) from \( y \) is the correct operation.
Therefore, the only correct expression for \( x \) is:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
1. Start with the given equation:
[tex]\[ y = a x^2 + c \][/tex]
2. Isolate the \( x^2 \) term:
[tex]\[ y - c = a x^2 \][/tex]
3. Divide both sides by \( a \):
[tex]\[ \frac{y - c}{a} = x^2 \][/tex]
4. Take the square root of both sides to solve for \( x \):
Since taking the square root can result in both positive and negative roots, we get:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
So, the correctly solved equation for \( x \) is:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
Let's cross-check the provided options:
- \( x = \pm \sqrt{a y - c} \): This is not correct because it suggests multiplication inside the square root in a form not derived from the equation.
- \( x = \pm \sqrt{\frac{y - c}{a}} \): This is indeed the correct solution.
- \( x = \sqrt{\frac{y}{a} - c} \): This is wrong because the term \( c \) should be adjusted for multiplication/division prior to isolating \( x \).
- \( x = \sqrt{\frac{y + c}{a}} \): This is incorrect since subtracting \( c \) from \( y \) is the correct operation.
Therefore, the only correct expression for \( x \) is:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.