Questionb)
d)
Short Answers:
1) Given the following list of transformations, state the equation of the arabola in vertax form:
-reflection about the -axis
vertical shift 2 units up
- vertical shilal shift 2 un
horizontal stretch by a fa
- Vertical stes
- Vertical stretch by a factor of 3
vertex form equations [2T]:
Studdy Solution
STEP 1
1. The problem involves transforming a basic parabola using a series of transformations.
2. The transformations include reflection, vertical shift, horizontal shift, and vertical stretch.
3. The goal is to write the equation of the parabola in vertex form after applying these transformations.
STEP 2
1. Start with the basic parabola equation in vertex form.
2. Apply the reflection about the x-axis.
3. Apply the vertical shift.
4. Apply the horizontal shift.
5. Apply the vertical stretch.
6. Write the final equation in vertex form.
STEP 3
Start with the basic parabola equation in vertex form:
Initially, the vertex is at the origin, so and :
STEP 4
Apply the reflection about the x-axis. This changes the sign of the entire function:
STEP 5
Apply the vertical shift 2 units up. This adds 2 to the function:
STEP 6
Apply the horizontal shift 2 units right. This changes to :
STEP 7
Apply the vertical stretch by a factor of 3. Multiply the entire function by 3:
STEP 8
Write the final equation in vertex form. The vertex form of the parabola after all transformations is:
The equation of the parabola in vertex form after applying the given transformations is:
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