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SAT Math skill page

SAT Quadratic Word Problems Practice

Translate word problems into quadratics, then use the form that answers the question fastest.

Practice quadratic word problems in Dolphin SATPractice questions
12-18 min practice time3 questions on pageAdvanced Math
Practice time12-18 min
Question bank3 questions
Best forAdvanced Math

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
A rectangle has length x + 3 and width x. Which expression gives its area?
  2. 2x + 3
Show answer and solution
Correct answer

Solution walkthrough

  1. Area is length times width, so x(x + 3) = + 3x.
Question 2 of 3Medium
A ball height is modeled by h = - + 6t. At what positive time is the height 0?
  1. 1
  2. 3
  3. 6
  4. 9
Show answer and solution
Correct answerC. 6

Solution walkthrough

  1. Set - + 6t = 0, factor t(6 - t) = 0, and use the positive nonzero time t = 6.
Question 3 of 3Hard
A quadratic has zeros 2 and 8. What is the x-coordinate of its vertex?
  1. 3
  2. 4
  3. 5
  4. 6
Show answer and solution
Correct answerC. 5

Solution walkthrough

  1. The vertex lies halfway between the zeros, so (2 + 8) / 2 = 5.

Avoid these traps

Common mistakes on this skill

Keeping every algebraic root without checking context

Time, length, and quantity restrictions can make one mathematical root impossible in the situation.

Confusing a zero with the vertex

Zeros mark where the modeled output is 0; the vertex marks a maximum or minimum.

Study plan

How to practice this skill in Dolphin

  1. Define the variable and identify what the output represents.
  2. Choose a quadratic form that exposes the needed feature: zeros, vertex, or initial value.
  3. Solve and then reject any result that violates the units, domain, or physical context.
Practice quadratic word problems in Dolphin SAT

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Skill cluster

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FAQ

Questions about SAT Quadratic Word Problems Practice

Which quadratic form is best for a word problem?

Factored form exposes zeros, vertex form exposes a maximum or minimum, and standard form exposes the initial value when x = 0.

Why might a quadratic model produce an invalid root?

The equation extends beyond the real situation, where negative time, length, or count may be impossible.