Write an equation of the parabola, in vertex form, that is a) Narrower than y=3x2 and is translated 4 units right and 1 unit down b) Congruent to y=0.5x2 with a maximum value of -4 at x = -2

Q: b) Draw the parabola with a minimum value of -8, zeros at 2 and -2 and y – intercept of -8.

A: Answer

Q: As arch is in the form of parabola with its axis vertical. The arch is 10m high and 5 at the base.…

A: Topic:- application of geometry

Q: Give the property that defines all parabolas.

A: A parabola is a plane curve and it is mirror-symmetrical and approximately it can be in the shape of…

Q: .what does the axis of symmetry do to the parabola?

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Q: The chord of a parabolic arch is 10 cm and is 12 cm from the vertex. Calculate the perimeter of the…

A: The formula for perimeter of parabola is P=12b2+16a2+b28aln4a+b2+16a2b, where a is the distance of…

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: If the line X equals three is the axis of symmetry of a para bola , Which coordinates below could be…

A: The axis of symmetry is a line, that divides the parabola into 2 equal halves. For the parabolas of…

Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 208 feet.…

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Q: Find the equation of parabola given these three points using quadratic formula. (1,27) (18,45)…

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Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: The path of the basketball through the hoop is modeled by the parabola,

Q: Create a two-way tunnel parabolic tunnel, given the dimensions, 16 feet by 34 feet, in standard and…

A: X is half of traffic width , 34 - 58 feet is 17 to 29 feet now we will allowable vehicle height as…

Q: Find the value of x in the rhombus. (3x²-6x) (4x² -27) ° X=

A: According to properties of rhombus, The diagonal bisect the angle. Opposite angles are equal.

Q: The vertical line passing through the vertex of a parabola is called the ......... .

A: Given The vertical line passing through the vertex of a parabola is called the ......... .

Q: .כ Find the ared of a parabola which is inscribed in a rectangle 40 cm long and 25 cm wide.

A: We know are of parabola is( 2/3) ×b×h Where b is base of parabola and h is height of parabola.

Q: Any point on the parabola can be labeled (x, y), as shown. 4 3 2 (*, y) ¢ -6 -5 -4 -3 2 - 1 2 3 4 5…

A: According to figure equation of parabola in standered form X2=4bYnew equation of…

Q: Find the standard equation of a parabola that has a vertical axis and satisfies the given…

A: Given:To Find the standard equation of a parabola that has a vertical axis and lineformula of…

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9−x2…

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Q: A rectangle is inscribed in the parabola y=8– x - such that one side lies on the x-axis and two…

A: Answer

Q: Find the vertex of the given parabola. Give all values correct to 3 decimal places. y = 7x2 - 8x +…

A: A detailed solution is given below

Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

Q: In Exercises 17–30, find the equations of the parabolas satisfying the given conditions. The vertex…

A: Given vertex (0,0) and directrix y=-0.16 We know the standard form of parabola with vertex at origin…

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: At the center of the lobby of a hotel is an artificial pond in the shape of an octagon serving as an…

A: Given:

Q: The vertical line passing through the vertex of a parabola iscalled the_________

A: Solution:GivenThe vertical line passing through the vertex of a parabola is called the ...........

Q: Find the standard form of a parabola with the following properties: Center at the origin…

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Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: A parabola with a negative latus rectum has endpoints at (5, 1) and (5, -11) Where is the vertex? *

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Q: A rectangular object 25 m wide is to pass under a parabolic arch that has a width of 32 m at the…

A: The arch can be modeled by the vertex form of a parabola centered at the origin with the base being…

Q: How many arrangements can be made using 2 letters of the word HYPERBOLAS if no letter is to be used…

A: To find the number of arrangements which can be made using two letters of the word HYPERBOLAS if…

Q: Define the term parabola?

A: Given: The term parabola.

Q: A pair of buildings on a college campus are shaped and positioned like a portion of branches of the…

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Q: Determine the coordinates of points A and B on a parabola y midpoint of AB is as close as possible…

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Q: Show the figure or model of a rectangular object 25 m wide is to pass under a parabolic arch that…

A: given that Parabolic arch has a width 32m at the base and height 24m at the center Vertex of…

Q: Determine the coordinates of points A and B on a parabola y AB is as close as possible to the…

A: Please refer the attached image for complete solution.

Q: How is the distance between vertices for hyperbola equal to 2a?

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Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 136 meters.…

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Q: Prove analytically that the midpoint of the hypotenuse of a right triangle is equidistant from the…

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Q: Explain why a line in hyperbolic geometry must contain two distinct ideal points.

A: We have to answer given Questions.

Q: 3. Find the dimensions and area of the largest rectangle having its two lower corners on the x- axis…

A: The given problem is solved below in detail.

Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: Show that,the area bounded by the parabola y^2 =4ax and a double ordinate is two third of the…

A: Let the parabola be y2=4ax Also let x =b be any double ordinate.Since the curve is symmetric about…

Q: The cable of a suspension bridge is in the form of a parabola. The towers supporting the cable are…

A: Given that The cable of a suspension bridge is in the form of a parabola. The towers supporting the…

Q: Find the shortest distance of the point (10,4) to the parabola y=x2

A: Consider a  point on parabola  y=x2. Distance of this point with (10,4) s2=(x-10)2+(y-4)2…

Q: Find an equation of the parabola that is symmetric about x-axis, has its vertex at the origin and…

A: Since we know that standard equation of the parabola that is symmetric about the x-axis and has…

Q: Find the shortest distance of the point (6,3) to the parabola y=x2

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Q: 3. Express the quadratic in vertex form. Make sure to clearly show every step in completing the…

A: Given equation is y=2x2-12x+16 express it in vertex form

Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 260 meters.…

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Q: Find the vertex and length of the latus rectum for the parabola. y = (x - 2)2 - 9 Vertex: (x, y) = (…

A: Topic = Parabola

Q: At the center of the lobby of a hotel is an artificial pond in the shape of an octagon serving as an…

A: Given that there is an artificial pond in the shape of an octagon. Also given that the distance…