a. Find the coordinates of the vertex of the parabola y = ax2 + bx + c, a ≠ 0. b. When is the parabola concave up? Concave down? Give reasons for your answers.

Q: What is the equation of a parabola with vertex at (0,0), opens to the left and the length of latus…

A: Explanation: Given that,  Vertex of the parabola is (0,0) and the length of the Latus Rectum is 6…

Q: 3. The towers supporting the cable of a suspension bridge are 1200 m apart and 170 m above the…

A: Solution:-   First we are draw a rough diagram based on the given problem.      Both towers are…

Q: 16. The standard form of the parabola is (y – 5)² = 12(x + 3). Solve the following. a. Vertex b.…

A: a) vertex If the equation of parabola is (y-h)2=4p(x-k) the vertex is (k,h) for the given equation,…

Q: 79. Given an equation of a parabola (x – h) = 4p(y – k) or (y - k) = 4p(x – h), how can you…

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Q: 3) Assume that the parabola y=x is translated so that its vertex is (5,-4). If the parabola is…

A: According to question given that  y=x2, vertex is (5,-4)

Q: 5. What point is the vertex of the parabola?

A: The vertex of a parabola is the point where the parabola crosses its axis of symmetry.   If the…

Q: Given the general form of a parabola x2+6x-24y+4=0, what is the x coordinate the vertex? h=_____.

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Q: given the equation of parabola y^2 -8x -4y -20=0,find the length of latus rectum

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Q: 2=2X Find the point that is close' to the pont'(,4) on the parabola y

A: Explained below

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

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Q: If the axis of symmetry of a parabola is given by x = 4, is it possible for the directrix to have…

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Q: The parabola y = ax? + k has vertex (0, –1) and passes through the point (4, 2). Find its equation.

A: we have to find the equation of parabola

Q: Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and…

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Q: 4. What is the axis of symmetry of the parabola y = x = 7 x= -14 y = 28 Ox=28 O x²14x+28?

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Q: The Vertex and the value of 'p' of the given parabola (x – 5)² = 16(y – 9) are

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Q: What is the directrix of the parabola? (x – 4)? = 8 (y + 3) O x = -3 O y = -3 y = -5 x = -5

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Q: A parabola has an equation of x²-4y-2x+8=0. Find the length of the latus rectum.

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Q: How many points of intersection are there between the graphs of the hyperbola and ellipse? Зx2 — 4у?…

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Q: Given a parabola with vertex at (8,-4) and focus at (-4,-4), determine the equation of the parabola.…

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Q: The equation of the parabola y' = 4ax is in the standard form. FALSE O TRUE

A: The given equation of parabola is -  y2 = 4ax

Q: If the focus of a parabola whose vertex is at the origin and which opens down is (0, -4), what is…

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Q: If the intersection points of the hyperbola 3x² – y² = 11 and the line 2x + y = 10 are P and Q,…

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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: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: 11. Which of the following is the standard form of the equation of a parabola with a horizontal axis…

A: 11.    Standard form of the equation of a parabola with a horizontal axis of symmetry is given by:-

Q: if the point (a, b) is on the parabola y=6x^2-(5785/12) that is closest to the point (0,4) than a ?

A: Given, y=6x2-578512 suppose x,y any point closest to 0,4  D=x-02+y-42 put y in equation,…

Q: 16. Which equation represents the given parabola?

A: We want to find the equation of given parabola.

Q: Given the directrix and vertex, what would the equation of the parabola be? (1, 2) O (y – 2)² = 6 (x…

A: We have to find the equation of parabola

Q: What is the line that cuts a parabola into two equal parts? * Your answer

A: Topic:- geography      axis of symmetry: A line that divides the parabola into two equal halves and…

Q: the value of a in y=ax^2+bx+c and the vertex of the parabola are given. how many x-intercepts does…

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Q: If the focal length of a parabola is 6 units and the vertex is (3, 2), is it possible to determine…

A: Focal length of a parabola is 6 units and the vertex is (3, 2).

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given…

A: Plot the given points line joining focus and vertex is parallel to y axis. That means axis is…

Q: The vertex of the parabola is (1, 0), and the directrix is x = -0.5. Which form does the equation of…

A: From the given information the directrix is at x=-0.5. So it is a horizontal parabola The vertex…

Q: I dont understand if this is a completing a square problem and if so how i would go about solving…

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Q: A parabola is modeled with the equation x2 – 6x + 4y – 19 = 0. Which is the domain and range of the…

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Q: Use the given equation of a parabola to answer the questions. (x+ 2)? = 3 (y+ 4) What is the…

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Q: The towers supporting the cable of a suspension bridge are 1200 m apart and 170 m above the bridge…

A: Cable is 116 meters high at 120 meters away from the tower. Answer and explanation is given below

Q: The equation of the parabola r = 4(y– 2)² is opening

A: Note: Equation of parabola Direction where it opens y=ax-h2+k and a>0 Upward y=ax-h2+k and…

Q: Which are the foci for the hyperbola modeled by the equation (Y-32 (x-1)² _ -1? 36 13

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Q: Express your final answer in Mdx + Ndy = 0 1. Parabola whose vertex is at point P(13, 60).

A: The given data is: 1. Parabola whose vertex is at point P (13,60), Express your final answer in…

Q: How many derivations are required for the problem involving parabolas with axis parallel to the…

A: Since you have asked multiple questions, we will solve first one for you. If you want other question…

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

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Q: If we have a parabola with an axis of symmetry of x = 9 and it contains the point (-3, -12), what…

A: Given taht parabola is symmetric about the line x= 9

Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 O 6 4 O 3

A: The given parabola is: y2+3x-12=0

Q: 2. Find the point on the parabola x+y? 0 that is the closest to the point (0, -3).

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Q: For Exercise, write the standard form of the equation of the hyperbola subject to the given…

A: From the given statement, the corners of the reference rectangle are  (7,6), (-1,6), (7,0), (-1,0)…

Q: What is the equation of a parabola with vertex at the origin, and focus is on the x-axis that passes…

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Q: 3) Assume that the parabola y=x is translated so that its vertex is (5,-4). I If the parabola is…

A: Let's see a concept of stretch of function y=f(x). Say y = f(x) is parent function.

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.