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Math  /  Algebra

Questiony=−(x)2−4y=-(x)^{2}-4
Match the equation to its description.
Reflected over xx axis and left 4
Reflected over xx axis and right 4
Reflected over xx axis and up 4
Reflected over xx axis and down 4 Scarleth S

Studdy Solution

STEP 1

What is this asking? Which description matches the given parabola equation? Watch out! Don't mix up what the negative sign in front and the negative sign inside the function do!

STEP 2

1. Analyze the reflection.
2. Analyze the vertical shift.

STEP 3

Alright, let's **break down** this equation, piece by piece!
We've got y=−(x)2−4y = -(x)^2 - 4.
Notice that *negative* sign hanging out in front of the x2x^2?
That's the big boss here, telling us that our parabola is **flipped**, or **reflected**, over the x-axis.
It's like looking at the parabola's mirror image!

STEP 4

Now, let's look at the −4-4 at the end of the equation.
This tells us about the **vertical shift** of our parabola.
Since it's −4-4, it means our parabola is shifted **down** by **4 units**.
Think of it like the whole parabola took an elevator ride, 4 floors down!

STEP 5

So, putting it all together, our parabola is reflected over the x-axis and shifted down by 4 units.
The correct description is "Reflected over xx axis and down 4"!

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