Let’s analyze the transformations step by step for the given function:

Given Function:

$f(x) = -5(x+4)^2 + 3$

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1. Reflection (Flip over an axis):

The negative sign outside the leading coefficient ($-5$) reflects the graph over the x-axis.

• Answer: x-axis

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2. Vertical Stretch:

The coefficient $-5$ represents a vertical stretch by a factor of 5.

• Answer: 5

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3. Horizontal Shift:

The term $(x + 4)$ means the function shifts 4 units to the left. The "+" inside the parentheses indicates movement to the left.

• Answer: 4 units to the left

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4. Vertical Shift:

The constant $+3$ outside the quadratic term shifts the graph 3 units up.

• Answer: 3 units up

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Final Answer Summary:

1. It flips over the x-axis.
2. It has a vertical stretch of 5 units.
3. It shifts horizontally 4 units to the left.
4. It shifts vertically 3 units up.

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Would you like me to expand further on any of the transformations?

Related Questions:

1. What is the vertex of this transformed parabola?
2. How does the vertical stretch affect the steepness of the graph?
3. What would happen if the coefficient $-5$ were changed to $+5$?
4. Can you write the transformation if the function were $f(x) = 2(x-1)^2 - 6$?
5. How do you determine if a parabola opens upwards or downwards?

Tip:

To easily identify horizontal shifts, look at the opposite sign inside the parentheses with $x$.