Example 1 Easy
A rectangle has length x + 3 and width x. Which expression gives its area?
- x^2 + 3x
- 2x + 3
- x^2 + 3
- 3x^2
Show answer and explanation
Answer: x^2 + 3x
Area is length times width, so x(x + 3) = x^2 + 3x.
SAT Math skill page
SAT Quadratic Word Problems Practice
Translate word problems into quadratics, then use the form that answers the question fastest.
12-18 min practice time 3 examples on page Advanced Math
What this tests
What to know for this SAT skill
- Build quadratic equations from word problems
- Interpret zeros, vertex, and intercepts in context
- Choose factored, standard, or vertex form
- Check whether the answer makes sense in the situation
Practice examples
Try a few SAT-style questions
Example 2 Medium
A ball height is modeled by h = -t^2 + 6t. At what positive time is the height 0?
- 1
- 3
- 6
- 9
Show answer and explanation
Answer: 6
Set -t^2 + 6t = 0, factor t(6 - t) = 0, and use the positive nonzero time t = 6.
Example 3 Hard
A quadratic has zeros 2 and 8. What is the x-coordinate of its vertex?
- 3
- 4
- 5
- 6
Show answer and explanation
Answer: 5
The vertex lies halfway between the zeros, so (2 + 8) / 2 = 5.
Quick drills
Practice this skill from more angles
Build quadratic equations from word problems
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Interpret zeros, vertex, and intercepts in context
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Choose factored, standard, or vertex form
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Check whether the answer makes sense in the situation
Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.
Avoid these traps
Common mistakes on this skill
Solving before naming the task
The SAT often hides the real skill inside familiar wording. Identify the rule, relationship, or question type first.
Choosing an answer that only partly fits
Many wrong answers are close. Check every condition in the question before committing.
Skipping the final check
Reread what the question asks for so you do not answer a nearby but different question.
Study plan
How to practice this skill in Dolphin
- Read the question and name the tested skill before looking at the choices.
- Write the equation, rule, or passage relationship in plain language.
- Eliminate answers that violate the setup or overstate the evidence.
- Review misses by writing the exact trap that pulled you toward the wrong answer.
Related practice
Build the surrounding skills
Skill cluster
Keep practicing SAT Math
FAQ
Questions about SAT Quadratic Word Problems Practice
What is the best way to practice SAT Quadratic Word Problems Practice?
Start with a few focused examples, review the mistake pattern, then mix the skill into full SAT practice so you can recognize it in context.
Why does this skill matter on the SAT?
It shows up in short, high-leverage questions where one missed rule or setup can quickly cost a point.
Can Dolphin SAT help me drill this skill?
Yes. Dolphin SAT can surface targeted practice, track missed questions, and help you review the patterns that keep repeating.