# How do you sketch the graph of #y=-3x^2# and describe the transformation?

See below.

The parent function:

looks like this:

graph{x^2 [-10, 10, -5, 5]}

This function has a negative sign which flips the graph along the x-axis. In other words, the parabola opens downwards. The 3 simply "tightens" the graph. The parabola gets narrower and grows faster.

graph{-3x^2 [-10, 10, -5, 5]}

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To sketch the graph of ( y = -3x^2 ) and describe the transformation:

- Start with the parent function ( y = x^2 ).
- Apply a vertical stretch by a factor of 3, which makes the parabola narrower.
- Reflect the parabola across the ( x )-axis due to the negative coefficient.
- Plot key points from the transformed function and sketch the resulting graph.

The transformation involves a vertical stretch by a factor of 3 and a reflection across the ( x )-axis compared to the parent function ( y = x^2 ).

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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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