What is the vertex of h(x)= 2x² -4x + 1? O A. (-2, 1) О В.(-0.25, 1) C. (1, -1) O D. (0.5, 0.25)

Q: use graphs to find approximate solutions.

A: use graphs to find approximate solutions. 2x=5

Q: Find the quadratic function y=ax2+bx+c whose graph passes through the given points.   ​(1​,−3​),…

A: Putting values of given coordinates one by one in above quadratic equation

Q: Find the points of intersection of the graphs of 2x 3y = -2 and 4.x – y = 6. %3D

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Q: True or False The y-coordinate of the vertex off1x2 = - x2 + 4x + 5 is f122.

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Q: fuo= x²-Gx +25 form Reurite in Vertex

A: Given,              f(x) = x2-6x+25

Q: Qn. The point of intersection of the graph of inequalities 2x+3y22 and X-yS3 is

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Q: Find the length of the chord intercepted by the circle x2+y2-x+3y-22=0 on the line y=x-3

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Q: If P(z) = 6 + z – 10z² represents the profit in selling z thousand Boombotix speakers, how many…

A: Given profit function is Px=6+x-10x2. Compute the derivative.…

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

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Q: [4] Find the equation of the quadratic function that has a vertex at (-2, 6) and contains the point…

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Q: 6) Discuss the concavity of the graph of ƒ (x) = x* – 2æ³ + 1 and find its points of inflection.

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Q: - For what value of k will the line kx + 5y = 2k be perpendicular to the line 2x - 3-y = 1?

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Q: 6. a. Clare is cycling at a speed of 12 miles per hour. If she starts at a position chosen as zero,…

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Q: 3. Find the values of b and c so f(x)=-8x² + bx+c has vertex (2, -7).

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the real number ( B) such that the line of symmetric equatic x - 3 == ) is parallel to the…

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Q: What is the length of the graph of y = In(x<+1) - x from x = 0 to x = 3?

A: Given  The graph equation is y=lnx2+1-x  from  x=0 to x= 3 .   Formula :- Arc length of curve…

Q: , and mz = X+ 20 A (3x) 20 -2 =180 x+20)° What is the value of x? What is the image of the point…

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Q: What is the value of a if the point (a, – 1) is on the line 3x – 2y = 8? a =

A: We have to find the value of a.

Q: Find the distance between u = 0 - 4 and z = 3 - 3 - 1 8

A: The distance between two vectors u=a1a2a3 and v=b1b2b3 is: d=b1-a22+b2-a22+b3-a32 The distance…

Q: Find the points on x=3-y^2 that are closest to the given point (1,0)

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Q: Draw the given optimization problem and solve. Find the area of the largest rectangle (in units)…

A: Since, We have to find area of the largest rectangle that fits into the triangle which sides form by…

Q: 2. F(-1, 1), G (1, 3), Н (4, -2), and I (2, —4)

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Q: Find the quadratic fúnction y= ax²+ bx +C whose graph pabses through the given points :(1,6),…

A: Given  The quadratic function y=ax2+bx+c and its graph is passing through the points 1,6,-1.-4  and…

Q: Find the area of the triangle that lies in the first quadrant (with its base on the x-axis) and that…

A: y=2x-4 and y=-4x+20 We need to find the area of the triangle that lies in the first quadrant (with…

Q: 3. What is the vertex of g (x) = x² + 5 ?

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Q: Find the point on the x-axis that is equidistant from the points (0,−1) and (5,−3)

A: To find the coordinates of the point satisfying the given conditions

Q: What is the vertex of g (x) = (x + 3)+3?

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Q: Q4B: Find min,max points for y = 2x- x2 %3D

A: The given function is y=2x-x2. Compute the critical point as follows. y'=0ddx2x-x2=02-2x=02x=2x=1…

Q: 3. Find the point (x1, x2) that lies on the line x + 5x2 = 7 and on the line x1 – 2x2 = -2. See the…

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Q: Which is an equation with a degree of 4, zeros located at (4, 0) and (3, 0) and a y-intercept…

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Q: Find the values of b and c f(x)=6x²+bx+c has vertex (7,-9)

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Q: The quadratic function y = ax2 + bx +c pass through (2, 1) and tangent to the line y = 2x + 4 at (1,…

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Q: Determine the values of b and c if f(x)=÷x* 1 x²+bx +c has vertex 3 ,6 5

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Q: Approximate the point of intersectión of the graphs of r and g. (x, y) = (

A: Given,

Q: How do you compute |PQ| from the coordinates of the points P and Q?

A: Suppose the coordinates of P and Q  are given as, a,b and c,d. Then to compute PQ⇀,   PQ⇀=c-a2+d-b2…

Q: A traffic report generated by the city council has determined that traffic increases or decreases…

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Q: an object is traveling on a path of y=sprt(x+3) where will the object be closest to (2,0)

A: We have to find the closet point to (2, 0)

Q: f(x) = 2x3+az? 12z has alocal maximum at z -2,then a

A: f(x)=2x3+ax2-12x  has a local maximum at x=-2then we have to find the value of a

Q: 10. Find the quadratic function for which the vertex is (-1,2) and contains the point (1,6)

A: Solve for the equation

Q: Find all points of discontinuity. g(x) = | x +3, if x>2 !! 8x, if x<2

A: Consider the provided function, g(x)=x2+3,   if x&gt;28x,        if x&lt;2 Find all the points of…

Q: 1. Pick a point where that is NOT on any of the lines: a = 0 y = 0 y = x y = -x 2. Find the equation…

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Q: A company manufactures running shoes and basketball shoes. The total revenue (in thousands of…

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Q: For what values of c is there a straight line that intersects the curve y = x' + cx' + 12x² – 5x + 2…

A: Given the equation of a curve , y=x4+cx3+12x2-5x+2. To find the value of c such that there is a…

Q: Find the point on the line x + 2y = 5 that is closest to the origin.

A: Let the point (x, y) on the given line x+2y=5  is closest to the origin (0, 0). observe that…

Q: 9) What is the vertex point f(x) (x+3)(x+7)

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Q: Draw the graph of the problem and comment the solution.                Max z = 10x1 +   20x2…

A: Problem isMAX Zx =  10 x1 + 20 x2subject to2 x1 + 6 x2 ≤ 102 x1 + 4 x2 ≤ 164 x2 ≤ 8x1    ≥ 5and…

Q: 6. Determine the equation of the quadratic function with vertex (5, -1) and y-intercept of 6.

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Q: Find b and c so that y 1x? + bx + c has vertex - (– 2, 0). С —

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Q: 1) Find all intercepts and test for symmetry. y = 3√9-x

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Q: Find the value of k such that the perpendicular distance of the point (2,k) from the line x - 2y =…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.