Quadratic Functions

Question 1

Vertex Form

Answer 1

• f(x) = a(x - h)² + k
• V = (h, k)
• Expand OR use the square

Question 2

Standard Form

Answer 2

• f(x) = ax² + bx + c
• h = -b/2a
• Complete the square OR Factor

Question 3

Factored Form

Answer 3

• f(x)= a(x - r)(x - s)
• h = (r + s)/2
• Expand OR expand then complete the square

Question 4

Minimum or Maximum

Answer 4

y = k

Question 5

|a| > 1

Answer 5

Shrinks horizontally, stretches vertically

Question 6

a > 0

Answer 6

Function opens up

Question 7

Expressing Domain

Answer 7

• Set Builder Notation: D = {x|x ∈ R}
• Interval Notation: x=(-ထ, ထ)

Question 8

Expressing Range

Answer 8

• Set Builder Notation: R = {y|a > y > b}, where a is the max and b is the min
• Interval Notation: y ∈ (a, b)

Question 9

Solving f(x) = ax² + bx + c

Answer 9

• x = (-b ± √Δ)/2a
• Δ (the discriminant) = b² - 4ac

Question 10

Value of Δ in a quadratic equation

Answer 10

• Δ > 0: Two distinct real solutions
• Δ = 0: Two equal real solutions
• Δ < 0: Two imaginary solutions

Question 11

Value of Δ when merging a linear and quadratic function

Answer 11

• Δ > 0: Two intersections
• Δ = 0: One tangent point
• Δ < 0: No common points

Question 12

Asymptotes of functions, f(x) = 1/(x - n) + k

Answer 12

• Vertical (VA): x = n
• Horizontal (HA): y = k