h(r) = r² + 11r – 26 1) What are the zeros of the function? Write the smaller r first, and the larger r second. smaller r = larger r = 2) What is the vertex of the parabola?

Q: 3. f(x) = -0.25x+ 8x - 2 Sketch: Opens: Vertex: Equation for Axis of Symmetry:

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Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

Q: C) lie in the parabola 16y = 160 – x². Find the maximum area of the triangle if side rtices B and C…

A: Sol

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

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Q: 3. Select the parabola that matches the quadratic relation y = x + 3x + 2. a. C. b. d.

A: We have to find

Q: 2 Find the vertex of the following parabola. a) f(r) = 22 – 2r + 5 b) f(r) = 322 + 12r – 9 c) f(r) =…

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Q: Which quadratic function has it's vertex at (-2,7) and opens down? a. y = -3(z + 2)² + 7 %3D b. y =…

A: Find which quadratic equation has its vertex at (-2,7) and opens down.

Q: 5. If f(x) = 2x2 +5 and g(r) = Vx – 2, find (f o g)(x) %3D 6. Find the vertex of the parabola f(r) =…

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Q: 45) Point M is the midpoint of AB. Find BM. 4x + 13 3x+17

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Q: 4. Find the quadratic function f(x) Arches if it passes through the points (0, 0), (1, 7.6), (9, 6).…

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Q: Q2. Use Lagrange Multiplier to find the point on the circle: x² + y² = 45 that are closest farthest…

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Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-…

A: Solving two equations

Q: The revenue from selling x units of a product us given by y=-0.004x^2+80x.How many units must be…

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Q: Given f(x) = x² – 16x + 55, a. Does the graph of the parabola open upward or downward? b. Find the…

A: Given f(x)=x2-16x+55 Let y=f(x) Then y=x2-16x+55…

Q: 18. Write the equation of a parabola with the shape as f(x)=-2x² but with the vertex (-3, 2).

A: Please refer the attached image for complete solution.

Q: A parabolic arch has an equation of 3x 2 + y – 300 = 0. a) What is the maximum height of the arch?…

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Q: Use the vertex (h, k) and a point on the graph (x, y) to find the Standard Form ( f(x) = a(x − h)² +…

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Q: IV. The path of a ball is given by y = - 16x? + 48x + 5, where y is the height of the ball and x is…

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Q: 25. What are the coordinates of the vertex of the parabola given the function f(x) = x2 + 8x-3 %D

A: f(x) = x2+8x-3 From the above equation we can see that the highest power of y is 1 and x is 2. This…

Q: Eind the quadratic function f/y) - oy2 + by + for which f/-1) - 5 f/1) - 3 and f/2)

A: The given quadratic equation is fx=ax2+bx+c                 …1 and f-1=5, f1=3 and f2=5. Substitute…

Q: 9. What is the value of k when writing the quadratic function y = x² + 10x – 17in vertex form? а. 22…

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Q: Given the parabola f(X) =-X²+10x +14, find the following for this parabola: A) The value of f(-1) =…

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Q: Sketch the parabola g(t) = -t2 + 4t - 3.

A: Sketch the parabola g(t) = -t2 + 4t - 3.

Q: Graph the parabola: f(x)=0.5x^2-2. Show all work.

A: We have given a function,

Q: 9) Find the point on the parabola y = 10-x² closest to the point (0, 5.5).

A: Given question:- Find the point on parabola y= 10-x2 closest to point (0,5.5)

Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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Q: ind the x-intercept(s) and the coordinates of the vertex for the parabola y=-x´-10x-25. If there is…

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Q: find the equations for the asymptotes. 4x2 + 24x - y2 + 4y + 28 = 0

A: Given:  4x2 + 24x - y2 + 4y + 28 = 0. To find: the equations for the asymptotes.

Q: Q.3 (a) for the following quadratic equation, determine (1) which way parabola open (ii) the…

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Q: Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x²-8x+7. If there is…

A: The given equation is;  y=x2-8x+7.

Q: Q,9. What point on the parabola y = v2x + 5 comes closest to the ori

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Q: Find the point on the parabola (y = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: Find the x-intercept(s) and the coordinates of the vertex for the parabola y=-x²+2x+3. If there is…

A: Given :y=-x2+2x+3

Q: 3) Find the vertex of the parabola f(x) = 4x² + 40x+104. Write in correct (x, y) form.

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Q: bétween the spheres and 2- + Y 4 if the dênsity at any point is equal to the square of its distance…

A: Given: The solid lies above the cone 3z=x2+y2 and between the sphere x2+y2+z2=1 and  x2+y2+z2=4  The…

Q: а. What is the maximum value of f(x) = -2x² – 4x + 3? The figure shows a segment joining the…

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Q: ind the vertex and the x-intercepts (if any) of the parabola. (If an answer does not exist, enter…

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Q: 11. If a projectile is fired straight upward from the ground with an initial speed of 96 feet per…

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Q: The parabola y = kx2 – 3x + (k+2) has two distinct real roots. What set of values can k be?

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Q: Find the x intercept(s) and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If…

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Q: d) What is the maximum height of the boarder?

A: Given, The gap is 2.2 m wide. And path modelled as h = -1.25d2 + 3.75d

Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-2y=4?

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Q: Given x2 = 4py with p&gt; 0, the parabola opens (upward/downward/left/right).

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Q: Fnd the x uterceptis) and the coordinates of the vertex for the parabola y=x+10x+25. If there is…

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Q: ich of the following is the value for æ for which the quadratic y = (x – 3)² + 4 s a turning point?…

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Q: Find the x-intercept(s) and the coordinates of the yertex for the parabola y =x´ +4x+4. If there is…

A: The given parabola is: y=x2+4x+4 To find the x-intercept and the coordinate of the vertex for the…

Q: 10. At what point on the parabola y = 3 x 2 + 2xisthetangentlineparallel totheline y = 10x -2? Use…

A: Given query is to find the point where tangent line to the parabola is parallel to the given line.

Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

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Q: Find the vertex for the parabola y = 0.01x2 + 0.6x + 100. Then determine a reasonable viewing…

A: Given: y=0.01x2+0.6x+100  To determine: The vertex for the given parabola &amp; graph of the given…

Q: Find the X-intercept(s) and the coordinates of the vertex for the parabola y=-x² - 4x - 4. If there…

A: topic- parabolas

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.