What is the vertex, the focus, directrix, and line of symmetry for 4 (y – 2) = (x + 1)2?

Q: 9ay? = (x-2a)(x-5a)". b. Find the perimeter of the loop of the curve

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Q: Use the algebraic tests to check for symmetry with respect to both axes and the origin.y = 1/(x2 +…

A: A function is symmetric with respect to the y-axis if f(x)=f(-x). Such a function is also called an…

Q: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

Q: Find the intersection points of the parabola above and the line -x+y=-4.

A: Given equation of parabola and the line are as below.

Q: What is the equation of the graph? A. y = 4cos (3x) В. у %3D 4sin (3х) С. у %3D Зсos (4x) D. y =…

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Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: Determine the graph of the equation a² + y² + 2² - 6x + 2y - 4z + 19 = 0. O Sphere O Point O Empty…

A: Given :x2+y2+z2-6x+2y-4z+19=0

Q: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

Q: A5: What is the minimum (perpendicular) distance from the point p = (-1,–2) to the line L := 4x = 14…

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Q: 6. y = x + 6x + 4 Axis of Symmetry: Vertex: Sketch:

A: Consider the equation: y=x2+6x+4 Compare the given equation with standard equation, y=ax2+bx+cAfter…

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: Sy < 1/3 x 1²x + 3 X y ≥ 2x 12 z -

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Q: The parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: Consider the graph of  y = ax2 + bx + c, where a = -3, b = 2 and c = 1.  Is the parabola concave up…

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Q: The hill has the shape of a cone, which in the XYZ system has the equation z = 4 - sqrt(x^2+y^2) A…

A: Given that hill has the shape of the cone given by z=4-x2+y2 and the tourist moves uphill whose path…

Q: Sketch the graph of y = m(r) in Figure 2. %3D 음-3, rS-1 m(x) = 4 %3D 1<r<5

A: Given,          mx=13x-3x≤-141&lt;x&lt;5

Q: How far from the y-axis is the center of the curve 2x2 + 2 y² + 10x – 6y – 55 = 0? %3D 2.50

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Q: find center verticals, foci and sketch its graph 2x2+3xy-4y2-3y+1=0

A: We are given : 2x2+3xy-4y2-3y+1=0 Plotting the graph, we have : This graph is a Hyperbola.

Q: What is the graph of the equation (x – xo)² + (y – yo)² + (z – zo)² = r² ? Sphere Cylinder Plane…

A: we have to cheek and find correct option

Q: Solve for the axis of symmetry and vertex for the following problems work on. y = z2 - 6z +8

A: Here to find the axis of symmetry =-b2a and , put this value in the equation to find the vertex.

Q: Graph: x2 + 4y2 + 10x + 24y + 45 = 0. Where are the foci located?

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Q: A parabola has an equation of y² = 4x. Find the nearest distance from the point (-3, 6) to the %3D…

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Q: Is the graph of r(z) = 47 - 212 + 9z – 2 concave up or down at the point with z-coordinate -1? %3D…

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Q: 5y=4 How would I make this into y=mx+b and graph this?

A: Consider the given equation,5y = 4Convert the above equation in form of  y = mx + b,

Q: For the parabola y=-4(x+1)^2 - 3, the range is...?

A: For  y=ax2+bx+c  with vertex      (x1  y1)

Q: Find the distance between the points of intersection of the graphs y = x² + 2 and y = 11. %3D

A: Given y = x2+2y = 11

Q: Find the following points of intersection. The point(s) of intersection of the parabola y = x2 + 2…

A: Given equation of parabola is y=x2+2 and equation of line is y=x+4. We have to find point of…

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

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Q: O Find All the ASymploles of the Cerve 3x3 +22y-7ay²+2y"-14x4+7y²+4x+5 =0-

A: Total Asymptods are 3 .

Q: =r = 2 and r = 4cos.

A: Intersection points in polar coordinates given in the form as (r, theta).

Q: 14. y = 2x- 12x + 10 Axis of Symmetry: Vertex: Sketch:

A: Given

Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find b and c so that y = 7x2 + bx + c has vertex (– 6, 2). - С —

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Q: Suppose the graphs of y = 5x? – 4x + 9 and y = x – 4x² – 2x + d intersect at a = 8. Find all…

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Q: What are the coordinates of the center of the curve x2 + y2 – 2x – 4y – 31 = 0?

A: Given, To find coordinates of center for the curve x2 + y2 – 2x – 4y – 31 = 0?

Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: First I have find the function f(x,y) and then decide the constraint.Then using Lagrange multipliers…

Q: For the parabola -2x 16y +4y2 + 13, for what value of y does r have a minimum?

A: This question is taken from the calculus in which we have to find the value of the y which makes the…

Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: Find the vertex, focus, and directrix for the following func (a) (y - 8)? = 16(x – 4) vertex : (…

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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-2y=4?

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Q: Find the point P on the parabola y = x2 closest to the point (57, 0). (х, у) %3D ]-«

A: Given the equation of parabolay=x2         ........(1)

Q: Suppose the graphs of y = 4x? 9x – 1 and y = x³ + bæ² + 17x + 111 intersect at x 2. %3D Find all…

A: Solution: The objective is to find the intersection points

Q: Find y, the shape is a trapezoid. (3x + 5)° (2y – 20)° (4x 30)

A: Sum of measurement of angles of a triangle is 180 degree

Q: Suppose the graphs of y = 5x? + 3x + 4 and y = x³ + bæ? – 78x – 158 intersect at x = – 9. Find all…

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Q: Consider the graph of (x^2) - (y^2/10) - (z^2/10) =1 1.What does the cross-section in the -plane…

A: The given equation represents a hyperboloid of two sheets.

Q: Find b and c so that y = – 10z² + bx +c has vertex (5, 10). b = c =

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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.