Find the vertex:g(x)=-2x^2 + 2x - 3

Q: Write in standard form of the quadratic function whose vertex is (-2,-1) and has a point of (0,3)

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Q: Graph f(x) = 3x3 – 5x2 – 27x + 45 in paper-pencil-ruler style.

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Q: Determine the vertex- f( x)= x^2 +4x +3 O (2-1) (-2, -1) O (3,-1) O (1,-2)

A: given equation of parabola f(x)=x2+4x+3 we know vertex is the maximum of minimum of a parabola,…

Q: Find two numbers whose sum is 40 and whose product is a maximum.

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Q: What are the points of intersection of the graphs of thefunctions f1x2 = - 3x + 2 and g1x2 = x2 - 2x…

A: f(x)=-3x+2 , g(x)=x2-2x-4

Q: Graph x < 0. + -5 -4 -3 -2 -1 0 +++ 1 3 4

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Q: Write the standard form of the quadratic function whose graph is a parabola with the given vertex…

A: We have given  vertex-52,0 and point -72,-163. If we have the vertex and one point of a parabola it…

Q: Write an equation of the quadratic function with the vertex at the point (-2, -5) and such that f(0)…

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Q: Sketch graph of Quadratic equation along its vertex -x²-2x+3

A: Given: y=-x2-2x+3

Q: give the domain and range of the quadratic function whose graph is described. Maximum = - 7 at x =…

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Q: Which quadratic function in vertex form can be represented by the graph that has a vertex at(4,-8)…

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Q: Find the rule of a quadratic function whose graph has the given vertex and passes through the given…

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Q: Write the standard form of the quadratic function that has the indicated vertex and whose graph…

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Q: Sketch the graph of ×to the power of 2-2x-3=y

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Q: Which quadratic function has a vertex point of (3, 5) and passes through the point (-2, 55)?

A: vertex point (3,5) (h,x) = (3,5)passing point (-2,55)

Q: Use the five-step strategy to graph f(x) = x3 - 3x2.

A: The given function is x3-3x2 The main objective is to plot a graph for the given function x3-3x2…

Q: Write equation in vertex for : y=-a(x-h)^2+k

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Q: Draw the graph of a quadratic function that has a vertex at (−2,5) and has a y-intercept of 3. Make…

A: Quadratic function and it's graph

Q: Find the vertex of the function: y = 2Vx + 9- 2 O (9,-2) O (-9,-2) O (-9,2) O (9,2)

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Q: What is the maximum product of two numbers whose sum is 9 ​? What numbers yield this​ product?

A: The sum of two numbers is 9.

Q: how to transform standard form of a quadratic function into the vertex form?

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Q: Give the domain and the range of the quadratic function whose graph is :Maximum = -6 at x = 10

A: we know that quadratic function domain is always x∈R, so domain will be x∈-∞,∞ if, maximum value of…

Q: Find two numbers whose sum is 20 and whose product is a maximum

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Q: Find the maximum product of two positive numbers with the sum of 300.

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Q: Use the vertex (1,6) and a point on the graph (6,-19) to find the equation of the quadratic…

A: Given: Vertex1,6Point on the graph 6,-19

Q: Find the equation of a quadratic function whose graphis a parabola passing through the points (0,…

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Q: The area of a rectangle is represented by 12x - x² where x is a side of the rectangle. For what…

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Q: Express the quadratic function -4x^2-20x+1 in vertex form

A: NOTE: Refresh your page if you can't see any equations. .

Q: Sketch the graph of ƒ(x) = x2 + 4/2x

A: Given: fx=x2+42x graph of given function can be drawn as below

Q: Write the standard form of the quadratic function whose graph is a parabola with the given vertex…

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Q: Suppose two numbers add up to 20. What is the maximum value of their product?

A: Given that: Two numbers add up to 20.

Q: Find the cubic polynomial whose graph is passing through the points

A: A cubic polynomial is a polynomial with the highest degree of the polynomial equal to 3. The…

Q: The profit from a grove of orange trees is given by x(230-x)  dollars, where x is the number of…

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Q: Find two numbers whose sum is 11 and whose product is a maximum.

A: Let x and y be the two numbersx+y =11y =11-xProduct is maximumTherefore, xy is maximumx(11-x) is…

Q: Write the equation of the quadratic function with vertex (2,-4) passing through point (0,6).

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Q: Solve in easy method by using graph

A: It is given that, the equation y=2x  and y=x+2 and            which equation represent the graph .…

Q: What is the maximum product of two numbers that add to 28? What numbers yield this product?

A: Given query is to find two numbers that add to 28 and their product will be maximum

Q: Find three numbers which add to 100 and whose product is maximized.

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Q: Divide the number 120 into two parts such that the product of one part and the square of the other…

A: To divide the number 120 into two parts such that the product of one part and the square of the…

Q: Determine the equation of a quadratic function in standard form given zeros x= -4, x = -2 and point…

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Q: Divide 9 into two parts such that the product of one by the square of the other is a maximum. What…

A: 9 is divided in two parts such that the product of one and the square of the other is maximum.

Q: Find two positive real numbers whose sum is 40 and whose product is a maximum.

A: A function f(x) is said to have a maximum value at a point c when the first derivative of the…

Q: Explain how to graph x2 + y2 = 1.

A: Given:Explain how to graph x2 + y2 = 1.

Q: Find two numbers whose sum is 50 and whose product is a maximum.

A: To find two numbers whose sum is 50 and whose product is a maximum.

Q: Determine the quadratic function whose graph is given below. 20- 10- -10 -5 0, - 2) 5 10 (-2,- 6…

A: given graph represent  a parabola open towards positive y axis

Q: Find two numbers whose sum is 11 and product is a maximum?

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Q: Find three positive numbers whose sum is 400 and whose product is a maximum. Answer (separate by…

A: Let the three numbers be x, y, z. The sum of numbers = 400. Therefore, x+y+z= 400.…

Q: Can you graph sq root (x2+1)?

A: the graph of the function is shown in figure below

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.