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

## What is an equation of a parabola with the given 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.

## How do you find the focus and directrix given the vertex?

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.

How do you find the vertex of a parabola using an equation?

How to find a parabola’s equation using its Vertex Form

1. Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola’s equation in the form: y=a(x−h)2+k.
2. Step 2: find the value of the coefficient a by substituting the coordinates of point P into the equation written in step 1 and solving for a.

### What’s the vertex on a graph?

The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.

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

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.

How do you calculate the vertex of a parabola?

In parabola, vertex is the measurement of the maximum or minimum point in a curve. Vertex of the parabola is defined by using the quadratic equation. Graphically, vertex of the parabola can be found by using the formula y = a(x – h) 2 + k Here, h,k are the vertex.

## What is a vertex and focus?

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## What is the equation for the focus of a parabola?

One standard form of an equation for a parabola showing the focus: (x-h)^2=4p(y-k), with (h,k) being the (x,y) coordinates of the vertex, parabola opens upwards, and the axis of symmetry is a vertical line thru the vertex.

What is the formula for a parabola?

A parabola is a mathematical concept with a u-shaped conic section that is symmetrical at a vertex point. It also crosses one point on each of the x and y axes. A parabola is represented by the formula y – k = a (x – h)^2.