Can just make up your data. Can ignore taking picture steps and all that. Just n
ID: 3283309 • Letter: C
Question
Can just make up your data. Can ignore taking picture steps and all that. Just need some help on how to do this even if not full solution.
25 PS The Drinking Fountain Model 1. Designers use computer-aided drafting and design (CADD) software to represent real objects on a computer display. CADD software lets them experiment with various shapes and designs without having to construct real, physical models. When the designer is satisfied, the software prints out detailed plans that a machinist or carpenter can use to build the real object. a) Take a picture or video of a drinking fountain in our school. Describle the interesting facts of the parabolic arch. /2 b) Trace your parabola onto a 8.5X 11 piece of graph paper. Place your axes on the graph paper ensuring that the vertex of your parobala is not the origin. Determine an appropriate scale and describe how you arrived at this scale given your parabola's realistic nature. /3 c) By estimating points on your parabola, model your parabolic relation with a quadratic function. Express your quadratic relation in vertex, factored and standard form. /4 d) Describe your parabola by commenting on all of its properties, i.e. Coordinates of the vertex, equation of the axis of symmetry, x-intercepts, direction of opening, maximum/minimum value and where it occurs /4 e) Explain how you would adjust your model to reflect higher or lower water pressure of the fountain. /3 f) Create an application question that a classmate would find interesting to solve. Provide a solution to your problem. /5Explanation / Answer
a)solution:
picture of drinking fountain looks like inverse parabola.
Interesting facts about parabola:
parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits any of several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
A parabola is the set of all points in the plane equidistant from a given line (the conic section directrix) and a given point not on the line (the focus).The line is called the directrix, and the point is called the focus. The point on the parabola halfway between the focus and the directrix is the vertex.
A parabola is a graph of a quadratic function, y = x2, for example. The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola which is parallel to the directrix and passes through the focus.
parabola is as a conic section, created from the intersection of a right circular conical surface and a plane which is parallel to another plane that is tangential to the conical surface.
Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, all parabolas are geometrically similar.
light that originates from a point source at the focus is reflected into a parallel ("collimated") beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with sound and other forms of energy. This reflective property is the basis of many practical uses of parabolas.
b) take the picture on paper , draw parabola matching with the picture where vertex is not the origin and give any scale for that graph for defining points of parabola based on parabola nature
c)estimate and note down points on your parabola graph in a table and
write parabola equation in quadratic equation form with the help of those points (generally parabola equation is in y= ax^2 + bx + c form)
then change that equation into vertex, intercept and standard forms
for example if y = ax^2 + bx + c is the standard form then
vertex form is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola
intercept form will be as y = a(x - p)(x - q) where p and q are the x-intercepts of the function
so represent your parabola equation into above 3 forms
d) refer to point (a) for describing properties of your parabola like coordinates of vertex, axis of symmetry, , x-intercepts, direction of opening, minimum/maximum values
Vertical parabolas give an important piece of information: When the parabolaopens up, the vertex is the lowest point on the graph — called the minimum, ormin. When the parabola opens down, the vertex is the highest point on the graph — called the maximum, or max.
The general form of the equation of a parabola is: Look at the coefficient of the term, that's the a, and... If a > 0 (positive), then the parabola opens upward and the graph has a minimum at its vertex. If a < 0 (negative), then the parabola opens downward and the graph has a maximum at its vertex.
We can identify the minimum or maximum value of aparabola by identifying the y-coordinate of the vertex. You can use a graph to identify the vertex or you can find the minimum or maximum value algebraically by using the formula x = -b / 2a.
e) adjust your parabola vertex so that you can reflect higher or lower water pressure.
for higher water pressure increase vertex hight(increase y value)
for lower water pressure reduce vertex hight(reduce y value)
f) create your own problem based on above to your friend