# How do you graph #f(x)=3x^2 + x - 5#?

Plot points, using a graphing utility, or manipulate the form of the equation so that it's elements reveal the graph's behaviors.

Plotting a few points is an easy method. Simply plug in some values for

When you plot these points, you get following. Note that the red values beneath the dots are in the form

Drawing a smooth line through them gives you the graph you are looking for. Using your graphing utility, like a Ti-83, is even better. Finally, you can manipulate the equation to give to information about the behavior of the parabola. This is known as graphing a quadratic function using transformations.

First, complete the square on the right side:

The *stretched* parabola, *to the left* by one-sixth. Finally, the *down* about

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To graph the function f(x) = 3x^2 + x - 5, you can follow these steps:

- Identify the vertex of the parabola using the formula x = -b / (2a), where a = 3 and b = 1.
- Substitute the x-value of the vertex into the function to find the corresponding y-value.
- Plot the vertex on the graph.
- Determine the direction of the parabola (upward or downward) based on the coefficient of x^2 (positive for upward, negative for downward).
- Plot additional points on either side of the vertex by choosing values of x and calculating the corresponding y-values using the function.
- Connect the points to form the graph of the parabola.

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When evaluating a one-sided 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 one-sided 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 one-sided 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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