1. Chapter 15 Review
Quadratic Functions

2. What is the name of the graph of a quadratic Function?
Parabola

3. What is the form of this quadratic equation?
𝑦=2 𝑥+3 2 −4 Vertex form

4. What is the form of this quadratic equation?
𝑦=2 𝑥 2 +3𝑥 −5 Standard Form

5. List the transformations for the following function:
𝑦=−2 𝑥 2 −5
Reflection over the x- axis
Vertical stretch by factor of 2
Vertical shift down 5 units

6. List the transformations for the following function:
𝑦= 𝑥+2 2
Vertical shrink by factor of 1/3
Horizontal shift left 2

7. List the transformations for the following function:
𝑦=− 4 𝑥 2 +3
Reflection over the x-axis
Horizontal shrink by factor of ¼
Vertical shift up 3 units

8. Write the quadratic Function in vertex form after the given transformations to the parent function:
Reflection across the x-axis, vertical shrink by ½ , horizontal shift left 7
𝑦=− 𝑥+7 2

9. Write the quadratic Function in vertex form after the given transformations to the parent function:
vertical stretch by 5 , horizontal stretch by factor of 2, vertical shift down 4
𝒚=𝟓 𝟏 𝟐 𝒙 𝟐 −𝟒

10. Convert the following from vertex to standard form
𝑦=2 𝑥 −6
𝒚=𝟐 𝒙 𝟐 +𝟏𝟐𝒙+𝟏𝟐

11. Convert the following from standard to vertex form.
𝑦= 3 𝑥 2 −12𝑥+1 𝒚=𝟑 𝒙−𝟐 𝟐 −𝟏𝟏

12. Find the AOS and vertex.
𝑦= 3 𝑥 2 −12𝑥+1 𝑨𝑶𝑺:𝒙=𝟐; 𝑽𝒆𝒓𝒕𝒆𝒙:(𝟐, −𝟏𝟏)

13. Find the AOS and vertex.
𝑦= 3 𝑥− 𝑨𝑶𝑺:𝒙=𝟒; 𝑽𝒆𝒓𝒕𝒆𝒙:(𝟒, 𝟔)

14. What is the formula we use to find the AOS of a quadratic function in standard form?
𝑥= −𝑏 2𝑎

15. Find the x and y intercepts for the quadratic function below:
𝑦= 𝑥 2 −4𝑥+3
X- intercepts: (1,0) and (3,0)
Y- intercept: (0,3)

16. Determine the given characteristics of the quadratic listed.
𝒚= 𝒙 𝟐 −𝟔𝒙+𝟏𝟑
Direction: up
Vertex: (3,4)
AOS: x=3
Domain: All real numbers
Range: 𝑦 ≥4
Min/Max? Where?
Int. of Increase: (3,∞)
Int. of Decrease: (-∞, 3)
End Behavior: 𝑎𝑠 𝑥 →−∞, 𝑓 𝑥 →∞
𝑎𝑠 𝑥 →∞, 𝑓 𝑥 →∞