How do you find the equation of a parabola given the vertex and focus?

How do you find the equation of a parabola given the vertex and focus?

If you have the equation of a parabola in vertex form y=a(x−h)2+k, then the vertex is at (h,k) and the focus is (h,k+14a). Notice that here we are working with a parabola with a vertical axis of symmetry, so the x-coordinate of the focus is the same as the x-coordinate of the vertex.

What is the equation of a parabola with a vertex at 2/3 and a focus at 6’3 )?

a=6−2=4 as y coordinates are the same. (y−3)2=16(x−2) is the equation of the parabola.

How do you find the equation of a parabola with the vertex at the origin?

The standard equation of a parabola with vertex at the origin and vertical orientation is 4py = x2, where p is the distance between the vertex and the origin. When the vertex is not at the origin, but at the point (h, k), the standard form of the equation of the parabola is 4p(y – k) = (x – h)2.

What is an equation of a parabola with the given vertex and focus Vertex 0 0?

The equations of parabolas with vertex (0,0) are y2=4px y 2 = 4 p x when the x-axis is the axis of symmetry and x2=4py x 2 = 4 p y when the y-axis is the axis of symmetry.

What is the equation of a parabola with vertex 37 and 57?

a = 5 – 3 = 2 as y coordinates are the same. Since the focus lies to the left of vertex, a = 2. (y – 7)^2 = 8(x – 5) is the equation of the parabola.

Which is the axis of symmetry of a parabola with equation x2 =- 4y?

y axis
Explanation: Because x is squared, we get two values of x (equal and opposite in sign) for a single y value. That makes y axis as the axis of symmetry.

What is the standard equation of a parabola with vertex at HK?

To graph parabolas with a vertex (h,k) other than the origin, we use the standard form (y−k)2=4p(x−h) ( y − k ) 2 = 4 p ( x − h ) for parabolas that have an axis of symmetry parallel to the x-axis, and (x−h)2=4p(y−k) ( x − h ) 2 = 4 p ( y − k ) for parabolas that have an axis of symmetry parallel to the y-axis.

How do you find the vertex of a parabola equation?

To find the vertex of a parabola, you first need to find x (or y, if your parabola is sideways) through the formula for the axis of symmetry. Then, you’ll use that value to solve for y (or x if your parabola opens to the side) by using the quadratic equation. Those two coordinates are your parabola’s vertex.

What is the equation of the parabola given?

The general equation of a parabola can be given as, y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax.

What is the equation of a parabola with vertex 3 7 and 5 7?

Since the focus lies to the left of vertex, a = 2. (y – 7)^2 = 8(x – 5) is the equation of the parabola.