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Understanding the Equations of Parabolas
A parabola is a curve in which each point is equidistant from the following points:
• fixed point (focus) and
• fixed straight line (directrix)
Focus and directrix calculator draw a straight line on it and then enlarge the focus point.
Then, it takes some measurements until you get another point with the exact distance between the focal point and the line.
The focus of a parabola calculator is to track them until they get a lot of points, then connect them to obtain a parabola!
Parabola is a U-shaped graph. Equations with the variable “x” to the second power are called quadratic equations, and their graphs are always parabolic.
This is a quadratic equation that a parabola calculator uses.
y = x2−2
The parabolic graph can change the position, direction, and latitude according to the coefficients x2 and x and constants. Since these parts of the equation are essential, they are named in the so-called standard form.
The standard form of the quadratic equation: y = ax2 + bx + c (where ‘a’ cannot be zero). Please note that “a” and “b” are coefficients, positive or negative. The value of c is a constant, and all these values affect the constructed parabola.
Common Forms of a Parabola:
These are some common forms of a parabola that the parabola calculator by calculator-online.net uses for showing the results for the given values.
|Form:||y2 = 4ax||y2 = – 4ax||x2 = 4ay||x2 = – 4ay|
|Vertex:||(0, 0)||(0,0)||(0, 0)||(0, 0)|
|Focus:||(a, 0)||(-a, 0)||(0, a)||(0, -a)|
|Equation of the directrix:||x = – a||x = a||y = – a||y = a|
|Equation of the axis:||y = 0||y = 0||x = 0||x = 0|
|Tangent at the vertex:||x = 0||x = 0||y = 0||y = 0|
Let’s look at a few fables and see what we can do.
1. Y = -12 (x + 34)2 + 8
· First, we know that the parabola is vertical (open up or down) because x is a square. Define it to be turned on because (-12) is a negative number.
· Then we can find the vertex (h, k) with focus and directrix calculator. For a vertical parabola, h is placed in square brackets, and since the pattern has a negative sign, we must accept the opposite meaning. Therefore, h = -34. K is outside, and the sign in the pattern is positive, so we leave it unchanged k = 8. So, our vertex is (-34, 4). This is a vertical parabola that opens downwards. Its hint is (-34, 4).
2. X = 1/4 (y – 99)2 – 8
· First of all, we know that this parabola is horizontal (it opens to the left or right) because y is a square. We can define it to open to the right because a (1/4) is positive.
· Then we can find the vertex (h, k) focus of a parabola calculator. For the horizontal parabola, h is outside the brackets, and since the pattern contains a positive element, we will leave it as it is. So, h = -8. k inside, and the sign in the pattern is negative, so let’s take the opposite approach. k = 99. So, our vertex is (-8, 99). This horizontal parabola opens to the right, with the vertex (-8, 99). For more info please visit: https://calculator-online.net/