For the function y=x2+x+2, which statements are true? Select all that apply. a.

Q: The average cost per hour in dollars of producing x riding lawn mowers is given by the following.…

A: We have to find - the number of riding lawn mowers to produce in order to minimize average cost,…

Q: Find the optimal solution for the following function using the graph method? Min Z= 3X1 + 4X2 ST…

A: Given, Min Z=3x1+4x2          subject to X1+X2≤2                            X1+2X2≤5…

Q: f(x) = x(x+2)3 (x-4)2

A:

Q: If f(x) = 2x2 + 5 and g(x) = 3x + a, find a so that the graph of f ∘ g crosses the y-axis at 23.

A: fx=2x2+5  &  gx=3x+a Now, f∘gx=fgx=f3x+a=23x+a2+5

Q: what is the decreasing interval for the following function: y = -1/4x-5

A: The given function is: y=-14x-5 The function f(x) decreases when f'(x) < 0.

Q: The function f(x) = 2x²-3x+ k has a minimum -Find the value of k. 8. value of-

A: The function fx=2x2-3x+k has a minimum value 78. We have to find the value of k.

Q: Find an expression for the function whose graph is thegiven curve.   The top half of the circle x2+…

A: The given expression is Solve for y Subtract x2 from both sides

Q: Describe the concavity of the graph of f(x)=(x-2)5/3 And find the inflection points(if any)

A: See the attachment

Q: Select one of the following four sketches that describes the end behavior of the graph of the given…

A:

Q: Consider the function graphed at right. What are the X-intercepts of the function? Jo 9 8 76 5 What…

A: To find the x-intercept of the graph

Q: For each of the following , determine if the function describes a quadratic function or not. If it…

A: Second degree polynomial  is known as quadratic  function. Second degree polynomial f(x) is of the…

Q: For the function g(x) = - (x+4)2 +9, find each of the following by referring to the graph. (A)…

A:

Q: 6. For the function, y=x² - 4x - 5, complete the table then graph. -2 -1 1 4 2 10 -8 6 -4 -2 2468 10…

A: the equation given to us is  y=x2-4x-5

Q: Consider the function p(x) = 3x +x - 5x and the graph of y = m(x) below.

A: In the question it is asked to calculate the roots of p(x)=3x3+x2-5x and the graph m(x) given in…

Q: Given that f is a quadratic function with minimum f(x) = f(1) = 3, find the axis, vertex, range and…

A: Given, f is a quadratic function with minimum f(x) = f(1) = 3. We have to find the axis, vertex,…

Q: 6. Dharma graphed the parent function f(x) = x and h(x) on the same grid. If h(x) is steeper than…

A: The function f(x)=x represents linear equation. So, the graph of f(x) should be a straight line. If…

Q: J,Graph a piece-wise defined function. for -3 < x < -1 for -15x< 2 * + 4 for x2 2 n(x) 10 21 10-8 6…

A:

Q: If f(x) = 2x2 + 5 and g(x) = 3x + a, find a so that the graph of f ∘ g crosses the y-axis at 23

A: f(x)=2x2+5g(x)=3x+a

Q: Which graphs shows the function f (1): %3D 243z+2 17

A: Given

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Consider the following:  Find first and second derivative:…

Q: 5- For the function f(x)=x³/3(x²-3) – 3/2, determine: a- The domain. b- The x and y intercepts. c-…

A: Given problem:-

Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) the number of thousands of…

A:

Q: What is the minimum of the function y = -a + 3x for a <-1? %3D -4 -2 04 O2

A:

Q: What is the maximum of the function y = -x° + 3x for x > -1? O-4 O2 04 O-2

A: The given function is y=-x3+3x for x≥-1. Calculate the maxima of the function. Here we use the…

Q: Find the minimum value of the function f(x) = 2x² + 18.3x + 45 to the nearest hundredth.

A: Given function f(x)=2x2+18.3x+45

Q: A housing complex has 100 two-bedroom units. The monthly profit (in dollars) realized from renting…

A:

Q: For the function: f(x) = 31 + 3z2. %3D (a) identify the end behavior of the graph, (b) additional…

A: We have to find the nature of the given function then sketch the graph

Q: 30. f(x) = –(x – 4)² %3D - M,0)

A:

Q: An aircraft factory manufactures airplane engines. If x engines are made then the unit cost is given…

A: This question is related to maxima and minima of function, we will use differentiation to solve…

Q: Decide whether the following statement is true or false. If the discriminant b-4ac 0, the graph of…

A: GivenDiscriminant b2-4ac=0,   f(x)=ax2+bx+c will touch the x-axis at its vertex

Q: Given that a function y=x3, has a vertex at (-2,0), a local maximum at (-1,3), and a local minimum…

A: Given that a function y=x3, has a vertex at -2,0, a local maximum at -1,3, a local minimum at -3,-3,…

Q: For the function: y = 0.01x- 0.001x² Find the zeros, the vertex and the optimum value (max. or min.)

A: As per company guideline we are supposed to solve only one question at a time. For other question…

Q: Use the function’s equation .f(x) = 2x2 + 12x + 703, and not its graph,to finda. the minimum or…

A: Given function is fx=2x2+12x+703. We know that if fx=ax2+bx+c then maximum or minimum value occurs…

Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) - 0.01q? + 5q – 25, where q…

A: (A)

Q: (x2 – 6 if x < 1 12x – 5 if x 21' 8) Graph: f(x) Must show your work by creating a table of values.

A: To draw the graph of the given function first we find the function values corresponding to some x…

Q: Given the function y = -x³ +3x² – 3, select ALL of the statements that are true about the graph of…

A: Given the function

Q: STATE whether the following function has maximum or a minimum. Determine the value of the maximum or…

A:

Q: Find and label as minimum or maximum the stationary points for: f(x)-2x'-21x' +60х+10

A: Find the local maximum and minimum of the given function

Q: Find the following for the function. (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range n(x)…

A:

Q: What is the minimum of the function y = -x° + 3x for x <-1? -4 O-2 4. O 2

A:

Q: For the function f(x)=x3-3x what is the local maximum and where does it occur? what is the local…

A:

Q: 13) Given f(x) = 7x² – 4x – 2, without graphing, determine whether it has a maximum value or minimum…

A:

Q: What is the minimum of the function y = –x° + 3x for x < -1? O 2 O-4 4 O-2

A: We can solve it graphically. Graph of f for x&lt;=-1:

Q: Q4/A. Draw the graph, of the functions determined by the given formula y = V4 -x

A:

Q: Based on the following function: f (x) = -(x+ 2) - 4 (a) What is the vertex as an ordered pair? (b)…

A:

Q: t is the absolute minimum value of h(x) = -2x² %3D

A: Solution of the problem as follows

Q: Suppose a manufacturer of washing machines found that when the unit price is $x, the revenue R (in…

A:

Q: 4) y= V4x + 8 %3D y -6 -4 -2 4.

A:

Q: The axis of symmetry of the graph of f(x) = −2x² − 4 is the line y = 0. - Select one: True False

A: Given that the axis of symmetry of the graph of fx=-2x2-4 is the line y=0.

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.