for the given audratic equation determine, i- which way the parabolla opens ii- the cordinate of the vertex iii- the roots of the functions 1- y=x2-3x+2 2- y=2x2-3x+1

Q: The parabola y = ² is changed to the form y = a (x − p)² + g by translating the parabola 2 units…

A: The parabola y=x2 is changed to the form y=ax-p2+q by translating the parabola 2 units down and 3…

Q: Find the change of variable x = Py that transforms the quadratic form xTAx into yTDy as shown 2x? +…

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Q: Determine whether this is a parabola: y = 5a + 80x + 321 . O Parabola Not a parabola If it is a…

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Q: Which of the following properties satisfy the parabola with equation x² + 6x + 8y = 7 O v(3,2);…

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Q: Quadratic: y=" fincl Hhe 2irent graph and Parent dH ributes

A: Given that y=x2 Parent functions are the simplest form of functions.  The parent graph of the given…

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: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

Q: Find the axis of symmetry of the parabola x2-16 y-6 x+73 0 Select one: Oy= -8 O x= 3 Oy= 3 Ox= -3

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Q: 1. Sketch the quadratic y=x²-3x+2. Find the vertex of the parabola Enter your answer in the form:…

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Q: The parabola passes through the points (−3/2, – 1), (1, 5) and vertex is at (0, 4) with a horizontal…

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Q: A. Graph the following quadratic functions manually b sheet of graphing paper. 1. Axis of symmetry:…

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Q: Find a parabola with equation y = ax² + bx + c that has slope 10 at x = 1, slope -14 at x = -1, and…

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Q: If a parabola y=ax2+ky=ax2+k has vertex (0,−1)(0,−1) and passes through the point (4,2)(4,2). What…

A: A Parabola y=ax2+k       ...(1) has Vertex (0,-1) and Passes through the Point (4,2)

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

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Q: Find the directrix of the parabola described by the equation 6 (x – 3) + (y + 2)? = 0 O x = } O x =…

A: The  parabola with vertex at (h,k) and focus at (h-a,k) has a standard equation, (y-k)2=-4a(x-h) The…

Q: Complete the square for each of the following quadratic forms

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Q: Find the y-intercept and any x-intercept(s) of the parabola with equation y = -(x + 7) + 16. If the…

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Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: 10. Which equation represents the parabola that has been vertically stretched by a factor of 5,…

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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: Another constraint you can use to compute cubic splines is that the second derivatives of adjoining…

A: Consider the cubic polynomial  fx=⋮ai-1x3+bi-1x2+ci-1x+di-1, x∈(xi-1,xi]aix3+bix2+cix+di…

Q: est to the point 2, 2

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Q: Which point on the parabola is one of the roots of the quadratic equation y = -x² – 3r + 4? %3D -2…

A: The roots of the quadratic equation are given by the points at which its graph cuts the x axis.

Q: Find the equation of the parabola, y = ax2+bx+c, that passes through the points (−1, 6), (1, 4),…

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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.