How do you use the important points to sketch the graph of # f(x)= x^2+10x8#?
I would complete the square.
Completing the square will tell us the roots first of all, a nice basis to sketch the graph.
The completed square also gives a minimum (as the quadratic is a positive function).
Now we sketch a graph, by plotting these points and drawing a nice smooth curve. graph{y=x^2 +10x8 [14.68, 5.32, 37.21, 27.21]}
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To sketch the graph of ( f(x) = x^2 + 10x  8 ), you can follow these steps:

Identify the important points:
 Vertex: Use the formula ( x = \frac{b}{2a} ) to find the xcoordinate of the vertex, where ( a = 1 ) and ( b = 10 ). Then plug this xvalue into the function to find the corresponding yvalue.
 xintercepts: Set ( f(x) = 0 ) and solve for x.
 yintercept: Plug ( x = 0 ) into the function to find the ycoordinate.

Plot the important points on the coordinate plane.

Determine the direction of the parabola by considering the coefficient of ( x^2 ). Since ( a = 1 ) (positive), the parabola opens upwards.

Sketch the curve through the important points, making sure it curves smoothly.

Optionally, you can find additional points by choosing other xvalues and calculating the corresponding yvalues using the function. This helps in ensuring the accuracy of the sketch.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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