Finding the Focus, Directrix, and Axis of Symmetry of a Parabola Example 1  Summary and Q&A
TL;DR
This content explains how to find the focus, directrix, and axis of symmetry of a parabola by using the given equation.
Key Insights
 βΊοΈ The formula x  h^2 = 4Cy  K is used to find the focus, directrix, and axis of symmetry of a parabola.
 ππ° The values of H and K being zero indicate that the vertex of the parabola is located at (0, 0).
 π The value of C is found by setting 4C equal to four, and dividing both sides by four to get C equal to one.
 ποΈ The focus of the parabola is one unit above the vertex, at (0, 1), and the directrix is a horizontal line at y = 1.
 βΊοΈ The axis of symmetry of the parabola is the vertical line x = 0, which cuts the parabola in half.
 π The absolute value of C represents the distance between the vertex and the focus.
 π€ If C is negative, it means the parabola opens downwards instead of upwards.
Transcript
so we're being asked to find the focus directrix and axis also called the axis of symmetry uh for the following Parabola so solution so before we go further let me let me write down the formula right so this is x  h^ 2 = 4 C * y  K that's the formula we're going to use here for this Parabola right this type of Parabola either opens up or it opens... Read More
Questions & Answers
Q: How do you find the vertex of a parabola?
The vertex of a parabola can be found by setting H and K in the equation x  h^2 = 4Cy  K equal to zero, giving the coordinates of the vertex as (0, 0).
Q: How is the value of C determined in the equation?
The value of C is determined by setting 4C equal to four, which implies that C is equal to one. This indicates that the parabola opens upwards.
Q: Where is the focus of a parabola located?
The focus of a parabola is located at a distance of one unit above the vertex, in this case at (0, 1). The focus is always inside the parabola and the parabola opens towards the focus.
Q: What is the significance of the directrix in a parabola?
The directrix is a horizontal line that is located behind the parabola. In this case, the directrix is at y = 1. It helps to define the shape and position of the parabola.
Summary & Key Takeaways

The equation x  h^2 = 4Cy  K is used to find the focus, directrix, and axis of symmetry of a parabola.

The vertex of the parabola is found by setting H and K equal to zero, giving the coordinates (0, 0).

The value of C is determined by setting 4C equal to four, and dividing both sides by four to find C equal to one.

The focus of the parabola is located at (0, 1), and the directrix is a horizontal line at y = 1.

The axis of symmetry is the vertical line x = 0, which cuts the parabola in half.