## How do you find the standard form of a parabola given the Directrix?

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 a Directrix equation?

If F is the focus of the parabola, V is the vertex and D is the intersection point of the directrix and the axis of symmetry, then V is the midpoint of the line segment ¯FD . The equation of the directrix is of the form y=c and it passes through the point (1,6) . Here, c=6 . So, the equation of the directrix is y=6 .

**How do you find the standard form of the equation of the parabola with the given characteristics?**

Summary: The standard form of the equation of the parabola with the given characteristics and vertex at the origin & Directrix: x = -4 is x = y2 /16.

**What is the standard form of parabola?**

If a parabola has a vertical axis, the standard form of the equation of the parabola is this: (x – h)2 = 4p(y – k), where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h, k + p).

### What is the standard equation of parabola?

The standard equation of a parabola is y2 = 4ax. The axis of the parabola is the x-axis which is also the transverse axis of the parabola. The focus of the parabola is F(a, 0), and the equation of the directrix of this parabola is x + a = 0.

### How do you find the standard form of an equation of the parabola?

For parabolas that open either up or down, the standard form equation is (x – h)^2 = 4p(y – k). For parabolas that open sideways, the standard form equation is (y – k)^2 = 4p(x – h). The vertex or tip of our parabola is given by the point (h, k).

**How do you determine the equation of a parabola?**

– y = x 2 − 3 x − 3 – y = − ( x + 2) 2 − 1 = − x 2 − 4 x − 5 – y = ( x − 2) ( x + 6) = x 2 + 4 x − 12

**How to find the equation of a parabola?**

We can use the vertex form to find a parabola’s equation. The idea is to use the coordinates of its vertex ( maximum point, or minimum point) to write its equation in the form y = a ( x − h) 2 + k (assuming we can read the coordinates ( h, k) from the graph) and then to find the value of the coefficient a .

#### How can you tell if an equation is a parabola?

Find the vertex. We’ll discuss how to find this shortly.

#### What is the purpose of a directrix in a parabola?

– Coordinates of vertex: (0, 0) – Coordinates of focus: (0, -a) – Equation of the directrix: y = a – Equation of axis: x = 0 – Length of the latus rectum: 4a – Focal distance of a point P (x, y): a – y