Equations from Function Graphs

Using the degree and leading coefficient, match the graph to an equation.

• y=-(x-1)²(x+2)²
• y=(x-1)²(x+2)²
• y=(x-1)(x+2)²
• y=-(x-1)²(x+2)²

Using the degree and leading coefficient, match the graph to an equation.

• y=(2x-1)(x+2)²

• y=(2x-1)(x+2)³

• y=(2x+1)(x+2)²

• y=(2x+1)(x+2)

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)
• f(x) = (x-4)(x+1)²(x+2)(x+4)
• f(x) = (x-4)(x-1)²(x-2)(x+4)
• f(x) = (x+4)(x+1)²(x-2)(x-4)

Write the equation of the polynomial function with

zeros: 0, -2, 4 and the root of zero having an order of 3

• f(x) = x³(x-2)(x+4)

• f(x) = x³(x+2)(x-4)

• f(x) = x²(x-2)(x+4)

• f(x) = x²(x+2)(x-4)

Which equation MOST LIKELY matches the graph?

• y = x⁴ - x³ + 3x² + 2
• y = -x⁴ + x³ + 5x + 2
• y = x³ - 2x² + 1x + 3
• y = -x³ - 2x² + 1x + 3

f(x) = 2x³ - 3x² + 4x -10

State the maximum number of turns the graph of f(x) could make.

• 3

• 2

• 1

• 0

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 Degree: 7

• (x + 5)³(x - 9)²(x + 2)(x - 4)
• (x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷
• (x + 5)³(x - 9)²(x + 2)
• (x + 5)(x - 9)(x + 2)(x - 4)

Select all the even degree functions.

• A

• B

• C

• D

What is the leading coefficient?

• Positive 
• Negative

• y = x(x - 3)(x - 2)
• y = x(x - 3)² (x+2)
• y = x(x + 3)² (x - 2)
• y = -x(x + 3)² (x - 2)