How To Find The Focus Of A Parabola Calculator

Parabola Figurer

Created by Bogna Szyk and Wojciech Sas , PhD candidate

Reviewed past

Steven Wooding and Jack Bowater

Concluding updated:

January 18, 2022

Table of contents:

• What is a parabola?
• The parabola equation in vertex form
• Parabola focus and directrix
• How to utilize the parabola equation calculator: an example
• FAQ

Whatsoever time you come up across a quadratic formula you want to analyze, you'll notice this parabola calculator to be the perfect tool for you. Not only will it provide you with the parabola equation in both the standard form and the vertex grade, but likewise calculate the parabola vertex, focus, and directrix for you.

What is a parabola?

source: Wikimedia

A parabola is a U-shaped symmetrical curve. Its primary property is that every point lying on the parabola is equidistant from both a certain bespeak, called the focus of a parabola, and a line, called its directrix. It is also the curve that corresponds to quadratic equations.

The axis of symmetry of a parabola is always perpendicular to the directrix and goes through the focus point. The vertex of a parabola is the signal at which the parabola makes its sharpest plow; information technology lies halfway betwixt the focus and the directrix.

A real-life example of a parabola is the path traced by an object in projectile move.

The parabola equation in vertex class

The standard grade of a quadratic equation is y = ax² + bx + c. Yous can use this vertex calculator to transform that equation into the vertex form, which allows you to find the important points of the parabola – its vertex and focus.

The parabola equation in its vertex grade is y = a(x - h)² + one thousand, where:

• a — Same as the a coefficient in the standard form;
• h — x-coordinate of the parabola vertex; and
• k — y-coordinate of the parabola vertex.

You can calculate the values of h and yard from the equations below:

h = - b/(2a) grand = c - b²/(4a)

Parabola focus and directrix

The parabola vertex form reckoner also finds the focus and directrix of the parabola. All you lot have to do is to employ the following equations:

• Focus x-coordinate: 10₀ = - b/(2a);
• Focus y-coordinate: y₀ = c - (b² - 1)/(4a); and
• Directrix equation: y = c - (b² + 1)/(4a).

How to utilize the parabola equation figurer: an example

1. Enter the coefficients a, b and c of the standard form of your quadratic equation. Let's assume that the equation is y = 2x² + 3x - 4, what means that a = 2, b = 3 and c = -iv.

2. Calculate the coordinates of the vertex, using the formulas listed above:

   h = - b/(2a) = -3/4 = -0.75

   k = c - b²/(4a) = -iv - 9/8 = -5.125

3. Observe the coordinates of the focus of the parabola. The 10-coordinate of the focus is the same every bit the vertex'southward (ten₀ = -0.75), and the y-coordinate is:

   y₀ = c - (b² - 1)/(4a) = -four - (ix-ane)/viii = -5

4. Find the directrix of the parabola. You can either use the parabola estimator to do it for you, or you tin utilise the equation:

   y = c - (b² + 1)/(4a) = -4 - (9+1)/8 = -5.25

If you want to larn more coordinate geometry concepts, nosotros recommend checking the average rate of modify calculator and the latus rectum calculator.

FAQ

What is a parabola?

A parabola is a symmetrical U shaped curve such that every point on the bend is equidistant from the directrix and the focus.

How do I ascertain a parabola?

A parabola is defined by the equation such that every indicate on the curve satisfies information technology. Mathematically, y = ax² + bx + c.

How practice I calculate the vertex of a parabola?

To summate the vertex of a parabola defined by coordinates (10, y):

1. Find x coordinate using the centrality of symmetry formula:

   x₀ = - b/(2a)

2. Find y coordinate using the equation of parabola:

   y₀ = c - (b² - 1)/(4a)

How to calculate the focus of a parabola?

To summate the focus of a parabola divers by coordinates (x, y):

1. Find y coordinate using the formula y = c - (b² + 1)/(4a)
2. Find x coordinate using the parabola equation.

Bogna Szyk and Wojciech Sas , PhD candidate

What to input?

Standard form: y = ax² + bx + c

Results

Prove results using fractions?

Average rate of change Bilinear interpolation Catenary curve … 33 more

Source: https://www.omnicalculator.com/math/parabola

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