Chapter 15 Review Quadratic Functions

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

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

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

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

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

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

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=− 1 2 𝑥+7 2

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

Convert the following from vertex to standard form 𝑦=2 𝑥+3 2 −6 𝒚=𝟐 𝒙 𝟐 +𝟏𝟐𝒙+𝟏𝟐

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

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

Find the AOS and vertex. 𝑦= 3 𝑥−4 2 +6 𝑨𝑶𝑺:𝒙=𝟒; 𝑽𝒆𝒓𝒕𝒆𝒙:(𝟒, 𝟔)

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

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)

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? Min @4 Int. of Increase: (3,∞) Int. of Decrease: (-∞, 3) End Behavior: 𝑎𝑠 𝑥 →−∞, 𝑓 𝑥 →∞ 𝑎𝑠 𝑥 →∞, 𝑓 𝑥 →∞