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Chapter 1: Problem 57

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

Short Answer

Expert verified
The graph of the function \(h(x) = -(x-2)^2\) is a reflection of \(f(x) = x^2\) across the x-axis with a vertex shifted 2 units to the right from the origin, thus, located at (2, 0), and it opens downward.

Step by step solution

01

Graph the standard quadratic function

The standard quadratic function is \(f(x)=x^{2}\). This is a parabola that opens upwards with its vertex at the origin (0,0). Plot the graph of this function.
02

Shift the graph

According to our function \(-(x-2)^2\), we have \(h=2\), so the parabola will shift 2 units to the right. The vertex of the graph will be (2,0).
03

Reflect the graph across the x-axis

Since there is a negative sign in front of the function, the graph would reflect across the x-axis. Which means the parabola which was opening upwards will now open downwards.

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