SAT Quadratic Functions and Equations

Quadratics are tested in all three forms — standard, factored and vertex — because each form reveals something different: the y-intercept, the roots, and the vertex respectively. Choosing the form that already shows what is asked is most of the work.

Practise this skill freeHow the SAT is structured
MathAdvanced Math135 questions
The trap on this skill

Using the initial value or reading a coefficient instead of finding the vertex.

How this skill behaves

What 135 questions on it look like

88% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

42% of the bank for this skill is rated hard, so it rewards practice past the point where the basic form feels comfortable.

medium46%
hard42%
easy12%

Difficulty mix across the 135 questions in this skill.

From the bank

Three real quadratic functions and equations questions

Each one explains the credited answer and why every other option fails.

Advanced Math · medium

For the readingnook weekend scanner packing entry card, a value H is modeled by H = -3t^2 + 24t + 63, where t is measured in hours. What is the maximum value of H?

  1. A63
  2. B108
  3. C111correct
  4. D115
Why C is correct — and why the others are not

For H = at^2 + bt + c with a = -3 and b = 24, the vertex occurs at t = -b/(2a) = 4. Substituting t = 4 gives H = 111. The final step answers the prompt as it applies to Quadratic functions and equations. A final check is confirming that the selected expression has the same domain.

A. This value results from using the initial value or reading a coefficient instead of finding the vertex

B. This value results from using the initial value or reading a coefficient instead of finding the vertex

D. This value results from using the initial value or reading a coefficient instead of finding the vertex

Advanced Math · easy

For the observatory indoor badge counting batch card, a value H is modeled by H = -4t^2 + 8t + 209, where t is measured in hours. What is the maximum value of H?

  1. A209
  2. B214
  3. C215
  4. D213correct
Why D is correct — and why the others are not

For H = at^2 + bt + c with a = -4 and b = 8, the vertex occurs at t = -b/(2a) = 1. Substituting t = 1 gives H = 213. The key support is the way the item treats Quadratic functions and equations. A final check is checking the inequality direction after each operation.

A. This value results from using the initial value or reading a coefficient instead of finding the vertex

B. This value results from using the initial value or reading a coefficient instead of finding the vertex

C. This value results from using the initial value or reading a coefficient instead of finding the vertex

Advanced Math · hard

For the dockside upper handle scanning stock card, a value H is modeled by H = -3t^2 + 30t + 207, where t is measured in hours. What is the maximum value of H?

  1. A207
  2. B282correct
  3. C279
  4. D287
Why B is correct — and why the others are not

For H = at^2 + bt + c with a = -3 and b = 30, the vertex occurs at t = -b/(2a) = 5. Substituting t = 5 gives H = 282. The calculation or reading check points back to Quadratic functions and equations. A final check is matching the final number to the quantity described in words.

A. This value results from using the initial value or reading a coefficient instead of finding the vertex

C. This value results from using the initial value or reading a coefficient instead of finding the vertex

D. This value results from using the initial value or reading a coefficient instead of finding the vertex

135 questions on this skill, free to start.

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FAQ

Quadratic Functions and Equations questions

Which form of a quadratic should I use?

Factored form for roots, vertex form for the maximum or minimum, standard form for the y-intercept. Convert only when the form you have hides what you need.

How do I find the vertex quickly?

x = −b/2a from standard form, then substitute back for y. From vertex form it is read straight off.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Nonlinear Equations in One Variable127 questionsEquivalent Expressions120 questionsExponential Functions and Equations113 questionsPolynomial / Rational Expressions112 questions

Practise quadratic functions and equations until the trap stops working.

Real Digital SAT questions, the reasoning on every option, and a mistake bank that only clears when you get it right.

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