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

Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y – mx – b)^2 / (m^2 +1) = (x – h)^2 + (y – k)^2.

## 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.

## What is the equation of a parabola that opens left or right?

The standard form of a parabola that opens left or right, or a horizontal parabola, is as follows: x = a(y – k)2 + k.

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

Insert the vertex coordinates into the equation y= a(x-h)^2 + k, where h is the x-value and k is the y-value. The value of a comes from the original equation. y = 3(x+1)^2+5 This is the vertex form of the parabola’s equation.

## How do you find the equation of a parabola with only the vertex?

2 Answers. Use the general equation y=a(x−h)2+k, where (h,k) are the coordinates of the vertex. You already know that the y-coordinate of the vertex is k=−7. The x-coordinate of the vertex, h, is given to you indirectly: it is by symmetry the midpoint of the x-intercepts.

## WHAT IS A in Parabola equation?

For graphing, the leading coefficient “a” indicates how “fat” or how “skinny” the parabola will be. Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the “vertex”.

## What is ellipse equation?

The standard form of the equation of an ellipse with center (0,0) and major axis parallel to the x-axis is. x2a2+y2b2=1. where. a>b. the length of the major axis is 2a.

## How do you write an equation for a parabola?

This straight line outside the parabola is called the directrix. 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).

## What is the vertex form of a quadratic equation?

f (x) = a(x – h)2 + k, where (h, k) is the vertex of the parabola. FYI: Different textbooks have different interpretations of the reference “standard form” of a quadratic function. (h, k) is the vertex of the parabola, and x = h is the axis of symmetry.

## How do you shift a parabola up?

The function y=x2+b has a graph which simply looks like the standard parabola with the vertex shifted b units along the y-axis. Thus the vertex is located at (0,b). If b is positive, then the parabola moves upwards and, if b is negative, it moves downwards.

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