You are standing on the top of a 256 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is described by the following equation   (t)=-16t2+96t+256   The ball follows what type of trajectory?  (Line, parabola, etc.)   Why?

Q: Find an equation of the parabola with vertex (-5, -5) and directrix y = -11. D=0 ?

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Q: A cannonball fired out to sea from a shore battery follows a parabolic trajectory given by the graph…

A: a) To find the maximum height, we solve h'(x)=0 Answer(a): 2500 feet

Q: 2. You are standing on the top of a 256 feet tall building and launch a small object upward. The…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Q4) Find the y-intercept, x-intercept(s) and the vertex point for the parabola y = x2 + 6x + 5 then…

A: Given: Parabola: y=x2+6x+5 To Find:  The y-intercept, x-intercepts and the vertex point for the…

Q: What is the y-intercept of the graph of the parabola whose equation is y = x² – 2x- 8? A (4,0) B…

A: The point where a line or curve crosses the y-axis of a graph.  In other words: find the y value…

Q: Sarah dove off a diving platform into a pool. The dive as she returns to the surface can be modeled…

A: The modeled equation is:y=0.75x2-8x+15

Q: A Civil War cannon is placed at the base of a hill. The cannon is fired at an angle toward the hill.…

A: We will have to solve the given equations for x, to find the horizontal distance from the cannon…

Q: y=2x + 8x +9 Plot five points on the parabola: the vertex, two points to the left of the vertex, and…

A: Equation of parabola in standard form is  y = ax²+bx+c

Q: What are the coordinates of the vertex for the given equation in standard form? y=x^2+6x+5

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Q: The straight line EB cuts the parabola y = 2x2 - 3z - 2 at E and B and is parallel to y + r 0 F A 0…

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Q: y = 3x² + 6x – 5

A: The function is y=3x2+6x-5

Q: (i) Sketch the graph of y =|5x²– 14r – 3| graph meets the coordinate axes.

A: Given: y=5x2-14x-3 To express: (i) The given function in the form of p(x+q)2+r form. To sketch: (ii)…

Q: Q2/a/ Solve the equation |3x - 4| 7 b/ Find the equation of circle with center (-V3,-2) and radius…

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: An architect is designing a museum entranceway in the shape of a parabolic arch represented by the…

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Q: 0. Match the equation with its graph. &r-8y 16 A) C) B) D)

A: Topic:- linear equation

Q: The equation x2 +y² - 6x + 2y b describes a circle. If the radius of the circle is 4 units, what is…

A: We can find the value of b from the general equation of circle as below.

Q: Find the equation of the evolute of the parabola y? = 12x.

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Q: Match the equation with its graph. 4x2 - y2 + 4z = 0 y N +++ N

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Q: The daily profit, P dollars, of a ice cream vendor is mode-led by the equation P = -60(x-3)2 +140,…

A: Given equation for maximum profit is  P(x)=-60(x-3)2+140

Q: You are training your dog to catch a frisbee. You are playing in a large field, and you are standing…

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Q: b) Determine the concavity, Y-Intercept, X- intercept of the quadratic equation And sketch the…

A: Clearly shows the turning poin of the quadratic equation is (10, -50)

Q: Match the equation with its graph. y2 = 4x2 + 922 %3D 3 2-

A: This is the problem of 3 dimensional curve plotting. Based on the online available graph plotter we…

Q: A seagull sits atop a cliff and spies a fish under the water. To catch the fish, the seagull dives…

A: The given equation of path is y=2x2-28x+90.…

Q: - 7x + 12 = 0 %3D AY

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Q: Find the vertex of the parabola. y = x2 + 14x + 49 Please enter your answer as an ordered pair.

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Q: Graph the cardioid r a(1+ cost) , a < 0?

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Q: Match the equation with its graph. 15x - 4y? + 152? 2.

A: topic - sketch of a function

Q: What is the vertex of the parabola y = (x – 1)2 – 3? %3D

A: In this question to find the vertex of the parabola. So here we compare the given parabola with the…

Q: Match the equation with its graph. y? = 4x2 + 9z2 %3D 3 2

A: To find- Match the equation with its graph. y2 = 4x2 + 9z2

Q: Match the equation with its graph. 15x2 – 4y2 + 15z2 = -4 3 2

A: -x2a2 + y2b2 - z2c2 = 1  , represents a hyperboloid with axis y=0.

Q: Match the equation with its graph. x2 y2 z2 = 1 16 56y 3 2- -3t 3 544 +

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Q: Match the equation with its graph. y2 - 4x2 + 9z2 %3D -3 32

A: Given that: y2=4x2+9z2

Q: What is the equation of the parabola with horizontal axis, vertex (-2,1), and passes through the…

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Q: You are training your dog to catch a frisbee. You are playing in a large field, and you are standing…

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Q: frisbee. You are playing in a large field, and you are standing next to your dog when you throw the…

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Q: I need to graph the equation 4y-2x=8

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Q: modeled by the equation f(x) = -0.00092 4 0 2088x in the direction of the hole, and landed 1o yards…

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Q: Match the equation with its graph. x2 y2 z2 + = 1 9 9 16 4 -5

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Q: Aubrey bought a plant and planted it in a pot near a window in her house. As the plant grows, its…

A: Given that Aubrey bought a plant and planted it in a pot near a window in her house. As the plant…

Q: If x² – 3r + 5, find (a) r- and y-intercepts. (b) f(1) (c) f(a) (d) the maximum or minimum, using…

A: The function is x2-3x+5 we can write it as =(x2-3x)+5=x2-3x+322+5-94=x-322 +114

Q: The skateboarder drops into a vert ramp, following a parabolar y=x^2- 2x-3. The slope of his path…

A: The given equation of Parabola y=x2-2x-3 is an open upward parabola with (0,-3) is a y-intercept…

Q: Find the zeros of y = (+3) (a 4). Then graph the equation.

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Q: y= Vx-3+4

A: Given the function We need to graph the above function.

Q: Find the axis of symmetry and vertex for the parabola y = 5? + 30x – 1.

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Q: Consider the graph of the equation -6y = 3x + 18. What are the x- and y- intercepts? Enter your…

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Q: Match the equation with its graph. y2 = 4x2 + 9z? y 4 3 6.

A: The general equation of a double cone is given by y2=Ax2+Bz2. where A and B are constants. The given…

Q: d. Find the equation of the vertical parabola that passes through the points: A = (6, 1), B = (-2,…

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Q: solve the equation and show your solution on the graph 3x+2y=1 2x-y=10

A: The given system of equations is, 3x+2y=12x-y=10 Solve the system as follows. From the second…

Q: Match the equation with its graph. x2y2 z2 +. 25 36 %D 16 ZA ZA 7A

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.