Find A Function That Describes The Bottom Half Of The Parabola x + (y - 1)^2 = 0 | Summary and Q&A

TL;DR

Learn how to find the equation for the bottom half of a parabola by solving a quadratic equation and using the square root function.

Key Insights

• 🤗 Parabolas can open up or down depending on the value of Y being squared.
• 👈 Similarly, the parabolas can open left or right based on the value of X being squared.
• 🥡 The equation for a parabola can be solved for Y by taking the square root of the squared X value.
• 🤗 The coefficient in the equation determines the direction the parabola opens. Negative opens left, positive opens right.
• ➖ The equation for the bottom half of a parabola can be found by subtracting X from both sides, taking the square root, and adding a minus sign.
• ➕ The equation for the top half of a parabola can be found by using a plus sign instead of a minus sign.
• 🫢 The standard form for a parabola that opens left or right is y - K squared equals 4C times x - H.

Transcript

find an expression for the function whose graph is the bottom half of this parabola so let's just think about parabolas for a minute before we jump into this problem so as a simpler example let's say you had x equals y squared this is a parabola that opens right and it looks something like this and if you were to solve this equation for y you would... Read More

Questions & Answers

Q: How can I find the equation for the bottom half of a parabola?

To find the equation for the bottom half, subtract X from both sides of the equation, take the square root, and add a minus sign to the result.

Q: What determines whether a parabola opens left or right?

The coefficient in the equation determines the direction: negative opens left, and positive opens right.

Q: Can I use the same method to find the equation for the top half of a parabola?

Yes, the process is the same, except you use a plus sign instead of minus to obtain the equation for the top half.

Q: Is it necessary to use the square root function to find the equation for a parabola?

Yes, since the parabola equation involves squaring, taking the square root is necessary to find the equation for each half.

Summary & Key Takeaways

• Parabolas are curves that can open up or down, left or right, depending on the equation.

• To find the equation for the bottom half of a parabola, subtract the value of X from both sides of the equation and take the square root, adding a minus sign to get the desired result.

• The same principles apply to finding the equation for the top half of a parabola; use a plus sign instead.