Questions: Consider the following function. r(x)=-x^2+6x-5 Step 4 of 4: Graph the parabola.

Consider the following function. r(x)=-x^2+6x-5 Step 4 of 4: Graph the parabola.
Transcript text: Consider the following function. \[ r(x)=-x^{2}+6 x-5 \] Step 4 of 4: Graph the parabola.
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Solution

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Solution Steps

Step 1: Identify the function

The given function is: \[ r(x) = -x^2 + 6x - 5 \]

Step 2: Determine the type of graph

The function \(r(x)\) is a quadratic function, which means it represents a parabola. We will use the Cartesian coordinate system to plot this function.

Step 3: Define the range for the plot

To graph the parabola, we need to choose an appropriate range for \(x\). Let's use the range \([-1, 7]\) for \(x\) to capture the vertex and the intercepts of the parabola. For \(y\), we will use the range \([-10, 10]\) to ensure the entire parabola is visible.

Final Answer

{"axisType": 3, "coordSystem": {"xmin": -1, "xmax": 7, "ymin": -10, "ymax": 10}, "commands": ["y = -x**2 + 6*x - 5"], "latex_expressions": ["$y = -x^2 + 6x - 5$"]}

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