Question 1Easier
Which of the following gives both zeros of ?
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Answer: B — 0 and 6
Setting gives , so . Therefore the zeros are 0 and 6.
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Quadratic equations — ACT practice questions
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- 45 questions on the paper
- 43 practice questions in the app
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Practice 43 Quadratic equations questions in the app
What this topic is
Quadratic equations on the ACT Mathematics test cover finding zeros, rewriting equivalent forms, and using a known root to find a missing coefficient.
A student must expand vertex form, complete the square or factor, apply the quadratic formula, and use root-coefficient relationships. Items typically ask which choice gives both zeros, which equation is equivalent after rearranging, or the value of a parameter that makes a given solution work.
Common traps include listing only one zero, dropping a sign when moving terms, and treating a squared binomial as already solved. Answer choices usually list pairs of roots, rewritten equations, or one coefficient.
Sample questions
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 2Easier
Which of the following is equivalent to ?
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Answer: A —
Adding 25 to both sides gives . The left side factors as , so .
Question 3Easier
One solution of the equation is . What is the value of ?
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Answer: C — 9
Substitute : .
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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