Quadratic Functions

a function that can be written in the standard form y = ax²+bx+c where a is not equal to 0, and where the highest power is 2

• a > 0 : graph opens up
• a < 0 : graph opens down
• IaI > 1 : graph is narrow
• IaI < 1 : graph is wide
• AOS / X value : x = -b/2a
• Y int : c
• Vertex : find X value and plug into equation

R(X) = (original price - X)(original # ppl +ppl expected to comeX)

y = ax²+bx+c

y = a(x - h)²+k

• a : width and direction
• h : horizontal shift
• k : vertical shift
• Vertex : (h,k)
• AOS : x = h

y = a(x - p)(x - q)

• X ints : p and q
• AOS / X value : x = p+q / 2
• a : width and direction
• Y int : (a)(p)(q)
• Vertex : find X value and plug into equation

• Write function
• Multiply using FOIL
• Combine like terms

• Write function
• Rewrite (x - h)² --> (x - h)(x - h)
• Multiply using FOIL
• Combine like terms