1. Fill in the chart for each of the following quadratic equations: Quadratic Function Direction of Vertex Axis of Maximum or Minimum Орening Symmetry Value a) y =x² -3 b) У %3 0.5(х — 4)? +3 c)y = -3(x +5)? - 2

Q: What will be the axis of symmetry, the line about which a figure or curve is upon itself, between…

A: Given :   y=4x-2

Q: Find the indicated maximum or minimum value of f subject to the given constraint. Minimum: f(x,y) =…

A:

Q: 1. Find the maximum and minimum points of the given equation: b. у%3D (х - 6)°(9 — х)

A: To find the maximum and minimum points of the given equation: y=(x-6)2(9-x)

Q: Determine the value of p (where Ip| corresponds to the distance from the vertex to the focus) of the…

A: Given: Vertex of parabola is 3, -6and y-intercepts are 0, -10 and 0, -2. To determine: Value of p.

Q: dr if F= and C is a piece of the parabola y=4-x² from the point (–1,3) to the point (2,0).

A:

Q: In the general form Ax + By + C = 0, can I immediately determine that theslope is A and the…

A: We will write the given equation in the slope-intercept form.

Q: Find the maximum value of r + y subject to the constraint a2 + y? = 18.

A: The function is given by fx, y = x+y                                          ..........1 The…

Q: * the lines 2x 3y 1 0 and 3x y 4 0 ie along diameters of a circle of circumference 10 n, then the…

A: The equation of a circle centered at h,k is x-h2+(y-k)2=r2 , where, r is the radius. If the radius…

Q: Sketch the lines 3x+ 4y 7 and x- 2y = 6, and find their point of intersection. Hint: Their point of…

A:

Q: Please

A: Now differentiate it with respect to y and equate it to 0.

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

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Q: Find AA, in lowest terms, if the graphs of the equations Ax−11y=−2 and −5x+13y=7 are

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Q: Find maximum and minumum values of f(x, y, z) = 9x – 18y +45z subject to the constraint x? + y² + z²…

A:

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function

A: We will first express the equation of the parabola in the standard form: y = f(x) = ax2 + bx + c. x…

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: Find the maximum and minimum values of the given quadratic form, 2x + 6y? subject to the constraint…

A: To find the maximum and minimum values of fx,y=2x2+6y2…1 subject to the constraint x2+y2=1.…

Q: For what minimum integer value of a, will the line ax+(a+1),y=18 (a> 0) have two intersection points…

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Q: Find maximum and minumum values of f(x, y, z) = 3x – 6y + 15z subject to the constraint x2 + y? + z2…

A:

Q: The maximum and minimum values of 2x + 3y subject to the constraint x + y = 1, where 0 ≤ x,0 ≤ y,…

A: Given that 2x+3y  subject to constraint x+y=1 where x≥0, y≥0.

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: 1. A In y= Ber? Ве

A: Solve the above questions.

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x? + y? +…

A: The given function is; f(x,y,z) = 8x-16y+40z

Q: Identify the x-intercept(s) of this parabola. 10 8- 6- 4- -6 -2 2. 6 -4 O (3. 0)

A: x-intercept is the point where the graph crosses the x-axis.

Q: Which of the following equations of parabolas has its vertex at (1, 2)? O y= 12 + 2x + 3 O y= r² +…

A:

Q: 1. Find the maximum and minimum points of the given equation: a. y = x3 – 3x b. y = (x – 6)2(9 – x)

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Q: Find maximum and minumum values of f(x, y, z) = 2 - 4y + 10z subject to the constraint a? + y? + z?…

A: If f is our function and g is the constraint. We can use Lagrange multiplier, c to equate the first…

Q: Find maximum and minumum values of f(x, Y, z) = 8x – 16y +40z subject to constraint x2 + y? + z2 =…

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Q: In Problem,describe the set of points defined by the equation(s). x=3 and z=1

A: Cosider : x=1 and  z= 1 In the 3D vector space, the point (a,b,c) is  described as  x=a , y = b, z=…

Q: Find maximum and minumum values of f(x, y, z) = 5x – 10y + 25z subject to the constraint æ? + y² +…

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Q: Find b and c so that y=11x2+bx+c has vertex (−7,4). b= c=

A:

Q: We have graphed various equations of the form Ax2 + By2 = C, where C is a nonzero constant. Now…

A: Given that, 2x2 + 3y2 = 0 We have to find graph of given equation. Square of number is always…

Q: Find b and c so that y = 8x² + bx + c has vertex (7,5). b C =

A: Here given that y=8x2+bx+c and has the vertex at the point (7,5) since the line of symmetry is the…

Q: Find maximum and minumum values of f(x, y, z) = 7x – 14y + 35z subject to the constraint x? + y? +…

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. 2(x -…

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Q: Find the minimum value of f subject to the given constraint. f(xy) = 3x +y -4xy; x+y= 24

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Q: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

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

A:

Q: The maximum value of the function f(x,y) = (xy) subject to the constraint %3D g(x,y) = + y? = 1, is…

A: Consider the given equation. fx,y=xy6x24+y2=1 Now, apply the Langrenges multiplier. Find the…

Q: Show that the lines with symmetric equations L1 : = = and L2 : 팡!%3D 부 =D 촬 %3D y-3 are skew.

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Q: Find b and c that Y= 8x2 +bx+c has vertex (4,0) b= c=

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Q: 8. Represent the following inequalities in the Cartesian plane. a) 증+치 y² 9. 0 - y 1+ 1+ 1+ 7.3…

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Q: Solve for the orthogonal traectories y = x2- cX

A: The orthogonal trajectory is a curve that intersects each of the family's curves at a right angle.…

Q: Find the absolute maxımum and minimum of f(r, y) = x² + y subject to the constraint 3x2 + 4y? = 5

A: To find the absolute maximum and minimum values of f(x,y) subject to constraint g(x,y).

Q: 2. Suppose that the graph of y = ax²+bx+c is a parabola which vertex is V (-3, 7), what is the…

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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: (a) Let f(x, y) = x² + 2y². Find the extreme values of f(x,y) subject to the constraint equation x²…

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Q: * the lines 2x • 3y + 1 = 0 and 3x - y - 4 = 0 ke along diameters of a circle of circumference 10 1,…

A: Given circumference of the circle  10π we know that circumference of the circle with radius r will…

Q: Find the maximum and minimum values (if such values exist) of f(x, y) = x² + 6y² subject to the…

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Q: Find the minimum value of f subject to the given constraint (x.y) = 2x2 +y?; 2x + 3y = 44

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