4 results

vertex - Highest point or where 2 curves meet

A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola

A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola and the lotus rectum.
Equation of a parabola given the vertex and focus is:
([I]x[/I] – [I]h[/I])^2 = 4[I]p[/I]([I]y[/I] – [I]k[/I])
The vertex (h, k) is 4, -2
The distance is p, and since the y coordinates of -2 are equal, the distance is 6 - 4 = 2.
So p = 2
Our parabola equation becomes:
(x - 4)^2 = 4(2)(y - -2)
[B](x - 4)^2 = 8(y + 2)[/B]
Latus rectum of a parabola is 4p, where p is the distance between the vertex and the focus
LR = 4p
LR = 4(2)
[B]LR = 8[/B]

if the vertex of a parabola is (4,9) what is the axis of symmetry

if the vertex of a parabola is (4,9) what is the axis of symmetry
[B]x = 4[/B]

Polygons

Free Polygons Calculator - Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Quadratic Equations and Inequalities

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax^{2} + bx + c = 0. Also generates practice problems as well as hints for each problem.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)^{2} + k

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.