DOK 3 Practice

Justify quadratic model choices and critique reasoning.

These questions emphasize evidence, error analysis, representation choice, and interpretation of quadratic models.

How to use this set

For analysis items, name the evidence: constant second differences, zeros, vertex, opening direction, or context meaning.

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Set Focus

Quadratic analysis and justification

DOK 3 questions reward precise reasons, not just calculations.

Justification

Use second differences and features as evidence.

Error analysis

Correct sign errors and lost solutions.

Comparison

Compare vertices, maximums, minimums, and forms.

Modeling

Connect roots and vertices to real-world meaning.

Practice Questions

Analysis and Model Choice

Check your answer first, then reveal the explanation when you want the model.

Question 1

Justify model type

A table has y-values 12, 7, 4, 3, 4 for equal x-steps. Which evidence best supports a quadratic model?

Question 2

Error analysis

A student says the zeros of (x - 7)(x + 2) are x = -7 and x = 2. What is the best correction?

Question 3

Representation choice

A graph shows x-intercepts at -4 and 2 and opens upward. Which equation could match the graph?

Question 4

Compare functions

Function A has vertex (2, -3). Function B is y = (x + 4)^2 + 1. Which statement is true?

Question 5

Context interpretation

The profit for selling x items is P(x) = -2(x - 40)^2 + 3200. What does x = 40 represent?

Question 6

Table comparison

Which representation most clearly shows the x-intercepts of a quadratic?

Question 7

Solve with structure

A student needs to solve (x - 5)^2 = 49. Which solution set is correct?

Question 8

Model choice

Which situation is best modeled by a quadratic function?

Question 9

Interpret intercepts

A rocket's height is 0 at t = 0 and t = 6 seconds. What does t = 6 most likely mean?

Question 10

Equivalent forms

Which form of f(x) = x^2 - 6x + 5 best shows the zeros?

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