For the following functions (a) tell whether the graph opens up or opens down, (b) find the vertex, and (c) find the axis of symmetry. 1. y= -3x² + 1 2. y = -2x2 – 1

Q: For the function y=x-1, graph the points with the domain of {0,4,6,8,9}

A: Domain: Set of values of x or independent variable for which the value of y or dependent variable…

Q: Starting with the graph of f(x)=9^x, write the equation of the graph that results from (a) shifting…

A: Starting with the graph of f(x)=9^x, write the equation of the graph that results

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

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Q: f(x) = (x + 4)(x − 2)^2 Determine the maximum number of turning points of the graph

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Q: I am having trouble finding the right points to graph this function.

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Q: Starting with the graph of f(æ) = 2", write the equation of the graph that results from a.…

A: Given: f(x) = 2x

Q: Describe the translation needed to obtain the graph of g(x) = 2X-4 from the graph of f(x) = 2*.…

A: Describe the translation needed to obtain the graph of g(x)=2x-4 from the graph of f(x) = 2x

Q: Starting with the graph of f(x)=5^x, write the equation of the graph that results from a. shifting…

A: Transformation of graph

Q: Starting with the graph of f(x) = 4", write the equation of the graph that results from a. shifting…

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Q: For the graph below, calculate the following quantities. y=#(x) y=g{x} y/(5) if y(x) = f(r)g(x) a.…

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Q: Starting with the graph of f(x) = 4ª, write the equation of the graph that results from a. shifting…

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Q: For the following graph of f(x), fill in the table for fx). 12 10 4

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Q: How can the graph of f(x) = -(x -1 ) 2 +6 be obtained from the graph of y = x 2?

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Q: Starting with the graph of f(x) = 8", write the equation of the graph that results from %3D a.…

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Q: For f(x) = 2x2 + 2 %3D Complete the table: -2 -1 1 Graph the equation by plotting two points: 7- 6-…

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Q: For the following exercise, sketch the graph of the equation. 43. g(x) = -

A: The function is  f(x)=2x3-12

Q: For the graph, calculate the following quantities.  1) y'(5) if y(x)=f(x)g(x) 2) y'(2) if…

A: Given the graph of functions f(x) and g(x). The function f(x)  has a point of discontinuity at x=3.…

Q: Starting with the graph of f(æ) = 3ª, write the equation of the graph that results when: (a) f(x) is…

A: The basic function here is f(x)=3x

Q: Starting with the graph of f(x) = 9", write the equation of the graph that results from a. shifting…

A: In case of upward or downward shifting magnitude of function f(x) increase or decrease respectoiely…

Q: For the following equations, graph the functions and check the symmetry. y = x2 + 1 y = 3x – 6 y =…

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Q: How can the graph of f(x) = -4|x| be obtained from the graph of y= Ixl?

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Q: Starting with the graph of f(x) = 2, write the equation of the graph that results from (a) shifting…

A: Given graph equation , f(x)=2x (a) shifting f(x) 1 units upward, y= f(x)+1 =2x+1. (b) shifting f(x)…

Q: Graph the following function accurately (find the vertex and plot another 4 points). f (x) = 2x² –…

A: Given the function f(x) = 2x2-12x+11

Q: Starting with the graph of f(x) = 3", write the equation of the graph that results from %3D a.…

A: Given query is to find the equation after performing indicated transformation.

Q: x2 - 9 f(x) = %3D x2 + 4x + 3

A: Given fx=x2-9x2+4x+3

Q: 4) y= V4x + 8 -2 9-

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Q: In sketching the graph of y=f(x) = – 3cos +)+4, we translate the graph of y = - 3cos s 5 by 4 units…

A: Transformation of graph

Q: Starting with the graph of f(x) = 9ª, write the equation of the graph that results from a.…

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

Q: For these problems, identify the simple function and describe the translation to that basic graph.…

A: We can answer the question as below

Q: use this graph off to find the solutions to f(x) = 0. 4 6 6 10

A: From the graph we need to find the solution of the equation f(x)=0

Q: For these problems, identify the simple function and describe the translation to that basic graph.…

A: We need to find the basic function and then the transformation involved to make basic graph a graph…

Q: Graph the following function. 20- y = 2x2 - 5 16- Use the graphing tool to graph the function. 12-…

A: given function is,                                                             now

Q: For the following exercises, consider the points on the given graphs. Use a calculator to graph the…

A: Solving through the graph and drawing the graph by putting some point

Q: Starting with the graph of f(æ) = 7", write the equation of the graph that results from (a) shifting…

A: When the graph is shifted a units to the upward then the function will be y=fx+a. When the graph is…

Q: starting with the graph of f(x)=4x, write the equation of the graph that results from a. reflecting…

A: given function                 f(x) = 4x

Q: Determine the x coordinate of the inflection point for the graph h(x) = x^2-3x^2+9x+8

A: In the mentioned equation, the term containing x2 is repeated two times. So we will treat the first…

Q: How is the graph of y = f(x+2) – 1 obtained from the graph of y = f(x)? %3D

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Q: For the following functions (a) tell whether the graph opens up or opens down, (b) find the vertex,…

A:

Q: for the graph below, draw on the same grid for the graph for the following function a) y = f(x+5);…

A: Given graph is                   from the graph we can find function as when -4≤x≤-2 graph passes…

Q: Graph. Ay 10- f(x) = 5x – 6 8- Use the graphing tool on the right to graph the equation. 6- Click to…

A: The given function is f(x)= 5x - 6 Or  y = 5x - 6 Compare with  y = mx +c Slope m = 5

Q: how can the graph of f(x)=1/(x-9)^2 + 7 be obtained from the graph of y= 1/x^2 ?

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Q: Use the graph below to fill in the missing values. fx} -1 4 f(0) = %3D f(x) = 0, x = %3D f-'(0) =…

A: The given graph is

Q: Starting with the graph of f(x) = 5ª, write the equation of the graph that results when: (a) f(x) is…

A:

Q: Starting with the graph of f(x)=6x, write the equation of the graph that results from (a) shifting…

A: Given:     f(x) = 6x

Q: Match the graph with the function. 2 3x i 2 III IV (a) y- (x + 1)? O1 OV (b) y- (x - 1)2 O II ON (c)…

A: To match the graph with the function. a y=x+12b y=x-12c y=x2-1d y=-x2

Q: Sketch the graph of the following fu f(x) = (x + 3)4 he correct graph below OC.

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Q: Consider the graphs of y1 = f(x) and y2 = f(2x + 7). Make a prediction about how these graphs are…

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Q: Starting with the graph of f(x) = 9, write the equation of the graph that results from a. shifting…

A: The graph of y=f(x)-a shifts a units downward to  the graph of y=f(x). Where a>0. The graph of…

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.