Table of Contents
How do you find the vertex focus and directrix of a parabola?
The standard form is (x – h)2 = 4p (y – k), where the focus is (h, k + p) and the directrix is y = k – p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y – k)2 = 4p (x – h), where the focus is (h + p, k) and the directrix is x = h – p.
What is the vertex of y x 2 3x 4?
The vertex is (-1.5, -6.25).
How do you find the focus and Directrix?
Focus & directrix of a parabola from the equation So the focus is (h, k + C), the vertex is (h, k) and the directrix is y = k – C.
What kind of function is this y x 2 3x 4?
quadratic function
Summary
| Description | English: Graph of quadratic function y=x²-3x-4. Made with Geogebra by Pitix (talk) 10:28, 25 October 2015 (UTC) |
|---|---|
| Date | 25 October 2015 (original upload date) |
| Source | Transferred from en.wikipedia to Commons. |
| Author | Pitix at English Wikipedia |
What is the vertex focus and Directrix?
The fixed-line is the directrix of the parabola and the fixed point is the focus denoted by F. The axis of the parabola is the line through the F and perpendicular to the directrix. The point where the parabola intersects the axis is called the vertex of the parabola.
What do you call the turning point of a parabola or the lowest or highest point of the parabola?
vertex
The vertex is the turning point of the graph. We can see that the vertex is at (3,1) ( 3 , 1 ) . The axis of symmetry is the vertical line that intersects the parabola at the vertex.
Is the vertex halfway between the focus and Directrix?
The point on the parabola halfway between the focus and the directrix is the vertex. The line containing the focus and the vertex is the axis.
What is the equation of the parabola in focus vertex form?
The equation of the parabola in focus vertex form is (x – h) 2 = 4p (y – k) The vertex is at (h,k) giving us h = 4, k = 6 The focus is located at (h, k + p). In this example the focus is at (4, 3) so k + p = 3.
How do you find the directrix and vertex of a parabola?
How to find the directrix, focus and vertex of a parabola y = ½ x 2. The axis of the parabola is y-axis. Equation of directrix is y = -a. i.e. y = -½ is the equation of directrix. Vertex of the parabola is (0,0). Put your understanding of this concept to test by answering a few MCQs.
What is the equation of the axis of the parabola?
The axis of the parabola is y-axis. Comparing the given equation with x 2 = 4ay. We get 4ay = 2y. a = 2/4 = ½. Focus is (0,a) = (0, ½ ) Equation of directrix is y = -a. I.e y = -½ is the equation of directrix. Vertex of the parabola is (0,0). Test your Knowledge on Parabola.
Which point is equidistant from the vertex of a parabola?
So the focus and directrix are equidistant from the vertex. A parabola is a locus of points equidistant (the same distance) from a line called the directrix and point called the focus.