in the formula y=a(x-h)^2 + k, i know a represents orientation, compression, and stretch. But i dont get the meaning of orientation. ?

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in the formula y=a(x-h)^2 + k, i know a represents orientation, compression, and stretch. But i dont get the meaning of orientation. ?

in the formula y=a(x-h)^2 + k, i know a represents orientation, compression, and stretch. But i dont get the meaning of orientation.

Posted 228 day ago

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Answers (10)

Amar Soni

Orientation means shifting of the towards x-axix or y-axis from the original position.

Posted 172 day ago

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Thank you Dr. Bob. I appreciate that.

Posted 223 day ago

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atta

This formula is called the standard form of a quadratic function expressed formally as y = f(x) = a(x +- h)^2 +- k, where a is the leading coefficient, h is the x-value of the vertex, and k is the y-value of the vertex (h, k) || x = -b/2a. In the formula a(x - h)^2 + k, the orientation is associated with the general structure of the equation relative to the xy plane; that is, on a graphical system with x/y coordinates, the function f(x) = a(x - h)^2 +-k = ax^2 - 2axh + (h^2 + k) => f(x) = ax^2 + bx + c || y = x^2. The parent function of the standard quadratic formula is merely f(x) = x^2, which is initially positioned at the origin. When discussing graphical orientation, the general structure of a function's parent or root must be defined first with symmetry; that is, the parent function f(x) = x^2 is symmetric with respect to the y-axis. However, every transformation of this parent function shifts its position on the xy plane by either a horizontal or vertical shift. The horizontal and vertical shift are defined as follows:

f(x - c) => Positive Horizontal Shift
f(x + c) => Negative Horizontal Shift
f(x) + c => Positive Vertical Shift
f(x) - c => Negative Vertical Shift

These are what constitutes the orientation of the standardized formula of the quadratic function, which is f(x) = a(x - h)^2 + k. In this case, the orientation of this function would be positive horizontal shift of h-units with an upward vertical shift of k-units thus, making this anonymous quadratic function positive with a rise on both endpoints of the graph of f || f(x) = a(x - h)^2 + k.

J.C

Posted 227 day ago

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pecks_tutoring

If a is positive, the parabola opens upward. If a is negative, it opens downward.

Posted 227 day ago

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Doctor Bob

Tom, your answers are terrific on this subject.

Posted 228 day ago

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since a change in the value of (a) will change the shape of the parabola graph, ORIENTATION means just that. It orients the position, location and shape of the graph.

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mjoelg

If a is positive, the parabola opens upward (i.e. the vertex is at the bottom). If a is negative, the parabola opens downward.

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math_fanatic

The formula for a parabola that I have is:
(x - h)^2 = 4c(y - k)
using basic algebra to solve for y you get: y = [1/(4c)](x - h)^2 + k
Therefore, a in your formula is 1/(4c) in mine.

The value of a =1/(4c) where c is the distance from the the vertex to the focus of the parabola. The greater the absolute value of a (or 1/(4c)) the narrower the parabola will be. The smaller the absolute value of a the wider the parabola will open up. I have not heard the terms orientation, compression, and stretch applied to the value of a before but the orientation (up or down) is determined by whether a is a positive or negative number. Positive it opens upward, negative it opens downward. I'm guessing that compression and stretch have to do with what I mentioned before. The greater the absolute value of a the more "compressed" the parabola will be and the smaller the value the more "stretched" it will be.

I have a worksheet that gives the different formulas for the different kinds of parabolas. It's a word file but the explanations are in terms of the formulas I'm familiar with and may be a little more complicated than what you're doing. If you want to take a look at it let me know.

Posted 228 day ago

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By the way, the absolute value of a determines compression and stretch, the value of h determines horizontal location of the vertex, and the value of k determines the vertical location of the vertex in the given formula.

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victorclaude

I am an English major; you do the math.

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