During this pandemic Mary and her friends decided to take a break from schoolwork and go on a hike up the Blue Mountain. When she was at the top of the mountain, she was able to view a valley, as seen below in Figure 1. She begun to visualise the shape when she realized that the mountain on the left forms a cubic function with the valley. Choose a suitable cubic function to answer the following questions: 1. Determine the maximum point of the mountain and the minimum point of the valley using the curve you have chosen. Hence calculate the height of the mountain if it measured by taking the height from the minimum point of the valley to the maximum point of the mountain. 2. Verify that the points found in part 1. is a minimum and maximum point. 3. Find the area under the mountain between two fix points of your choice that is feasible.

Q: Fit a second degree parabola to the following data :

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Q: A trough is 3 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end…

A: The given function is  and the interval is .The current situation can be represented as below.The…

Q: 1. Find the equation of the curve passing through the focus of the parabola (opens downward and…

A: Given that parabola is passing through (3,0) (1,-1/2). (4,-1/8)

Q: The following illustrates an application of optimization using parabolas. The concentration C in…

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Q: find the equation of the quadratic function/equation. and

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Q: I- Parabola 1. Determine at sight the direction in which the curve opens. Locate the vertex, focus,…

A: The equation of parabola is x-12=-8y+12

Q: The parabola y = x^2 is compressed vertically and translated down and right. The point (4, -10) is…

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Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

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Q: Determine the vertex for the following parabola. f (x) = 7x2 + 3x – 4 -

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Q: 18. a. The graph of a parabola touches the x-axis at x-4 and passes through the point (2,9).…

A: a. Since the parabola touches the x-axis at x = -4, we know that one of the roots of the quadratic…

Q: b) 16 4 y= -0.0519x +1.0777x - 7.4569x + 20.247x- 12.333 12 R = 0.6113 10 10 2. time Calculate point…

A: Given equation y = -0.0519x4 + 1.0777x3 - 7.4569x2 + 20.247x - 12.333

Q: Find the equation for the parabola that has its focus at the (−7/4,−9) and has directrix at x=15/4

A: Here we have to find equation of parabola with given focus and directrix.

Q: Determine the equation of the parabola graphed below. 5 4 3 2 1 0 1 2 3 4 5 6 7

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Q: (iii) (1) Find the x-intercepts of the parabola. Give your answers in decimal form, correct to two…

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Q: Determine the vertex of each of the following parabolas. Then write each function in graphing form.…

A: Vertex form : y=((x-h)2+k) where (h, k) are vertex coordinates.

Q: 4. Create a parabola that meets the following requirements: a. Vertex below the x-axis b. Concave up…

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Q: If the vertex of the parabola f (x)= x² +bx+c is at (7, -4), find b and c. (Note: a = 1).

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Q: 3. A parabola is symmetric under a line re ection. Each real root of the quadratic function…

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Q: What is the equation of the function for a parabola that moves 2 units to the right of the origin, 2…

A: Given parent function is f(x)=x2

Q: The following illustrates an application of optimization using parabolas. A rock is tossed upward.…

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Q: Follow the graph to answer the question.

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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.