Example 1 Easy
If x is positive and x^2 = 49, what is x?
- -7
- 0
- 7
- 49
Show answer and explanation
Answer: 7
The solutions to x^2 = 49 are x = 7 and x = -7. Since x is positive, x = 7.
SAT Math skill page
SAT Quadratic Equations Practice
Handle SAT quadratic questions by recognizing roots, factors, parabolas, and the meaning of each solution.
14-20 min practice time 3 examples on page Advanced Math
What this tests
What to know for this SAT skill
- Factor simple quadratic expressions
- Use zeros to solve quadratic equations
- Interpret roots in context
- Recognize when a quadratic model has two, one, or no real solutions
Practice examples
Try a few SAT-style questions
Example 2 Medium
If x^2 - 5x + 6 = 0, what is the sum of the two solutions?
- 2
- 3
- 5
- 6
Show answer and explanation
Answer: 5
Factor the equation as (x - 2)(x - 3) = 0, so the solutions are 2 and 3. Their sum is 5.
Example 3 Hard
The height h, in feet, of a ball t seconds after launch is h = -16t^2 + 64t. After how many seconds does the ball return to the ground?
- 2
- 3
- 4
- 8
Show answer and explanation
Answer: 4
Set h = 0: -16t^2 + 64t = 0. Factor to get -16t(t - 4) = 0, so t = 0 or t = 4. The return time after launch is 4 seconds.
Avoid these traps
Common mistakes on this skill
Forgetting the second solution
Quadratics can have two roots. Check whether the problem wants one root, both roots, or a contextual answer.
Dropping a negative sign
Factoring and expanding quadratics often hinge on signs. Test your factors by multiplying them back out.
Using a context-impossible root
In word problems, a negative time or length may be algebraically valid but not meaningful.
Study plan
How to practice this skill in Dolphin
- Memorize the factor patterns for simple trinomials.
- Practice setting each factor equal to zero after factoring.
- Connect roots to x-intercepts on a graph.
- For word problems, reject roots that do not make sense in context.
Related practice
Build the surrounding skills
FAQ
Questions about SAT Quadratic Equations Practice
Do I need the quadratic formula for the SAT?
It can help, but many SAT quadratic questions are designed for factoring, graph interpretation, or simple structure recognition.
What is a root of a quadratic?
A root is an x-value that makes the quadratic equal zero. On a graph, roots are x-intercepts.
Why are quadratic word problems tricky?
They often produce more than one algebraic solution, and you have to decide which one fits the situation.