Graphs of quadratic functions f(x)=ax 2 +bx+c.

Q: 14.What are the zeros of the function represented by the quadratic equation g (x) = 2x ?

A: Given that gx=2x2 find the zeros of the function

Q: quadratic function f(x) has its vertex at the point (1, −4) and one of its x-intercepts is (3, 0)

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Q: 2) Find the formula for a quadratic function that passes through the points (4, 3) and (2, o a as…

A: To Find :- The formula for a quadratic function that passes through the points (4, 3) and (2, 8) and…

Q: Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the…

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Q: Use a graphing utility to graph the quadratic function. Find the x-intercept(s) of the graph and…

A: Here given function fx=710x2+12x-45 Graph the function as shown below,

Q: A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is…

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Q: The graph of the quadratic function f(x) = cx2 + d has a vertex at (0,7) and passes through the…

A: Given quadratic function is- fx=cx2+d Since, y=fx Hence, y=cx2+d Since, the graph has a vertex at…

Q: An apple orchard produces a profit of $40 per tree when planted with 3200 trees. Owing to…

A: Let number of tree is x Profit peer tree is equal to 40-0.04x-3200 Hence, total profit Px is…

Q: -1 -2 |(1, -2) -3 -6 -8 -9 -10 -4 -3 -2 Enter the rule for the quadratic function shown in the graph…

A: Using our general form of the quadratic, y = ax2 + bx + c, we substitute the known values for x and…

Q: Use a graphing utility to solve x3 - 3x2 - 4x + 8 = 0.Round answers to two decimal places.

A: x3 - 3x2 - 4x + 8 = 0.

Q: 11.What are the zeros of the function represented by the quadratic equa g (x) =- (x-4)?

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Q: Rewrite the quadratic function in standard form. h(x) = 2x2 + 4x − 17 h(x) =        Give the…

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Q: 3 . Write the quadratic function C(x) - x -x- 57 in vertex f c(x) c(x) = (x- 1) - 6 リ4 c(x) - c(x) -…

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Q: Determine a quadratic function whose graph has x-intercepts of (6, 0) and (−4, 0). f(x) =

A: f(x) =(x+6) (x-4)

Q: What are the real root(s) of the quadratic equation whose related function is graphed below? A (3,0)…

A: The x-intercepts of the graph are the roots of concerned quadratic equation.

Q: Consider the quadratic function f(x) = 4x2 - 16x + 1000. Solve; a. Determine, without graphing,…

A: Given Data The function is f(x)=4x2-16x+1000.   (a) Differentiate the function f(x)=4x2-16x+1000…

Q: The graph of a quadratic function f(x) is shown above. It has a vertex at (2, 1) and passes the…

A: The graph of a quadratic function fx has vertex 2,1 and passes through the point 0,-1. Standard…

Q: The graph of a quadratic function intercepts the x-axis in two places and the y-axis in one place.…

A: We know that ,  The fundamental theorem of algebra states that you will have n roots for an nth…

Q: 6. (a) Graph the quadratic function f(x) = -x² + 2x – 3 by determining whether its graph opens up or…

A: Given: f(x)=-x2+2x-3

Q: Use a graphing utility to graph the quadratic function f(x) = x2 − 4x. Find the x-intercept(s) of…

A: Graph the function fx=x2-4x.   From the graph it can be seen that the x-intercepts are 0,0 and 4,0.

Q: Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the…

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Q: A quadratic function can be written in the form h(x)=k(x-a)(x-b) where a and b are the zeros in the…

A: Given, hx = kx-ax-b   Where a = -3  and b = -5  are the zeros of the quadratic function and k = 3.…

Q: A quadratic function has its vertex at the point (3, 8). The function passes through the point (4,…

A: Equation is a Parabola with vertex at ( h, k)

Q: A quadratic function has its vertex at the point (- 4, – 2). The function passes through the point…

A: In vertex form, (h, k) is vertex point.

Q: 5. sketch a possible graph of a quadratic function which has two real roots, a graph that opens…

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Q: quadratic functions into the vertex 2. f(x) = 2x² – 12x+ 19 %3D

A: Explanation of the answer is as follows

Q: Find a quadratic function f(x) = ax? + bx +c whose vertex is (2, 4) and whose y-intercept is (0,…

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Q: 2. What does the discriminant tell us about a quadratic function? Explain the three possible cases.

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Q: . Rewrite the quadratic function in standard form; f(x) = x2 − 16x + 68. b. Give the vertex point.…

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Q: The vertex of the quadratic function f(x) = 2(x – 1)2 + 6 is

A: We compare the equation with the vertex equation  y=a(x-h)2+k Comparing we get: h=1 and k=6

Q: Consider the Quadratic function f(x) = x - 3x – 40. Its vertex is ( Its largest x-intercept is x =…

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Q: In 1995​, the sports league introduced a salary cap that limits the amount of money spent on​…

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Q: If a quadratic function has the rule f(x) = (x – h)² + k, what will cause a horizontal translation?…

A: Given query is to find the correct answer for the horizontal translation.

Q: Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the…

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Q: 5. Sketch a possible graph of a quadratic function which has two real roots (one positive, one…

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Q: In 1993​, the sports league introduced a salary cap that limits the amount of money spent on​…

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Q: The vertex of the quadratic function f(x)= (x+6)^2 -2 is

A: The general form of the quadratic function is, y=ax-h2+k Here, (h,k) is the vertex. Consider the…

Q: Use the graph of the quadratic function f(x) = a(x- h)< +k to find the vertex, axis of symmetry, and…

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Q: The graph of a quadratic function f(x) is shown above. It has a vertex at (2, 1) and passes the…

A: It is an downward parabola whose general equation is of the form(x-h)2 = 4a(y-k)       ..(i)where…

Q: Determine a quadratic function whose graph has x-intercepts of (4, 0) and (−2, 0).   f(x) =

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Q: Identify the quadratic function from the graph y -2 -3 -2 -1 2 a) f(x) = x² – 4x + 5 b) f(x) = x2 –…

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Q: A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is…

A: For a quadratic function, the standard form is represented by the equation, y=ax2+bx+c and the…

Q: How do I solve this question step by step : Determine a quadratic function in vertex form given that…

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Q: Find two quadratic functions, one that opens upward and one that opens downward, whose graphs have…

A: A quadratic function with x-intercepts (-4,0),(5,0) then gives (x+4) and (x-5) are factors of…

Q: How do you find the largest open interval of the domain over which function is increasing? With the…

A: This parabola is facing downwards because the leading coefficient is = -1/2 which is negative.  So…

Q: the vertex of Quadratic function f( x) = 2x2 - 4x + 1 is : Select one: a. (1,-1) b. (-1,1) c. (-1,…

A: Given : f(x) = 2x2 - 4x + 1 Vertex of f(x) = ?

Q: 3. Express the quadratic function g(x)=-4x² +4x+5 in the form a(x-h)' +k by completing the square,…

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Q: The vertex of the quadratic function f(x) = 2x² + 8x+5 is a) (2,3) b) (-2,–3) c) (-2,3) d) (2,-3)

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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.