Problem 57
Question
Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$h(x)=-(x-2)^{2}$$
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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.
2Step 2: 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).
3Step 3: 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.
Other exercises in this chapter
Problem 57
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