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

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.

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

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.

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.