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Chapter 2: Problem 55

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$g(x)=(x-2)^{2}$$

Short Answer

Expert verified
The graph of function \(g(x)=(x-2)^{2}\) is a standard quadratic function shifted \(2\) units to the right from the vertex \((0, 0)\) to \((2, 0)\).

Step by step solution

01

Graph the standard quadratic function

Begin by graphing the standard quadratic function \(f(x)=x^{2}\). This is a parabolic graph where the vertex is at the origin \((0, 0)\) and it opens upwards.
02

Identify the transformation

In the transformed function \(g(x)=(x-2)^{2}\), we can see the quadratic function is not different, but an alteration on the x variable has been made. The form \((x-2)\) indicates the graph should be shifted 2 units to the right, as it comes in the form \((x-h)\) where \(h\) corresponds to the horizontal shift.
03

Graph the transformed function

Starting from the original function graph \(f(x)=x^{2}\), apply a shift of 2 units to the right to every point to obtain the transfromed function graph \(g(x) = (x-2)^2\). This moves the vertex of the parabolic graph to the point \((2, 0)\) and it still opens upwards.

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Most popular questions from this chapter

For people filing a single return, federal income tax is a function of adjusted gross income because for each value of adjusted gross income there is a specific tax to be paid. By contrast, the price of a house is not a function of the lot size on which the house sits because houses on same-sized lots can sell for many different prices. a. Describe an everyday situation between variables that is a function. b. Describe an everyday situation between variables that is not a function.

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graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$ \begin{aligned} x^{2}+y^{2} &=16 \\ x-y &=4 \end{aligned} $$
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