SAT quadratic equations practice

Recognize when a graph reveals a root, a maximum, or a minimum. Practice reading the right feature.

The idea to remember

Roots occur where y = 0. The vertex is a turning point, not usually a root. For y = a(x - h)² + k, the vertex is (h, k).

A worked example

For y = (x - 3)² - 4, the vertex is (3, -4). Setting y = 0 gives (x - 3)² = 4, so the roots are 1 and 5.

A common trap

The minimum value is -4, whereas the x-coordinate where that minimum occurs is 3. Read the noun in the question.

For a longer walkthrough, read SAT quadratics: roots, vertices, and what the graph means.

By Graph Math Practice editorial team · Reviewed 2026-09-05

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All 8 questions, with explanations

Work on paper or read at your own pace. Open each explanation after choosing an answer. These are the same original questions used in the interactive tool.

1. The function f(x) = (x - 2)² - 4 has two zeros. What is the greater zero?
1. 4
2. 0
3. 2
4. -14
Show answer and explanation
Answer: A. 4
Set f(x) to zero. Then (x - 2)² = 4, so x - 2 equals 2 or -2. The roots are 0 and 4. The greater zero is 4. On a graph these are x-axis crossings.
2. A model is given by y = -2(x - 2)² + 14. What is the maximum value of y?
1. 2
2. -14
3. 16
4. 14
Show answer and explanation
Answer: D. 14
The squared term is never negative, so -2(x - 2)² is never positive. Its largest value is zero when x = 2. Therefore the maximum y-value is 14, the height of the vertex.
3. The function f(x) = (x - 3)² - 9 has two zeros. What is the greater zero?
1. 3
2. -19
3. 6
4. 0
Show answer and explanation
Answer: C. 6
Set f(x) to zero. Then (x - 3)² = 9, so x - 3 equals 3 or -3. The roots are 0 and 6. The greater zero is 6. On a graph these are x-axis crossings.
4. A model is given by y = -2(x - 3)² + 19. What is the maximum value of y?
1. 21
2. 19
3. 3
4. -19
Show answer and explanation
Answer: B. 19
The squared term is never negative, so -2(x - 3)² is never positive. Its largest value is zero when x = 3. Therefore the maximum y-value is 19, the height of the vertex.
5. The function f(x) = (x - 4)² - 16 has two zeros. What is the greater zero?
1. 8
2. 0
3. 4
4. -26
Show answer and explanation
Answer: A. 8
Set f(x) to zero. Then (x - 4)² = 16, so x - 4 equals 4 or -4. The roots are 0 and 8. The greater zero is 8. On a graph these are x-axis crossings.
6. A model is given by y = -2(x - 4)² + 26. What is the maximum value of y?
1. 4
2. -26
3. 28
4. 26
Show answer and explanation
Answer: D. 26
The squared term is never negative, so -2(x - 4)² is never positive. Its largest value is zero when x = 4. Therefore the maximum y-value is 26, the height of the vertex.
7. The function f(x) = (x - 5)² - 25 has two zeros. What is the greater zero?
1. 5
2. -35
3. 10
4. 0
Show answer and explanation
Answer: C. 10
Set f(x) to zero. Then (x - 5)² = 25, so x - 5 equals 5 or -5. The roots are 0 and 10. The greater zero is 10. On a graph these are x-axis crossings.
8. A model is given by y = -2(x - 5)² + 35. What is the maximum value of y?
1. 37
2. 35
3. 5
4. -35
Show answer and explanation
Answer: B. 35
The squared term is never negative, so -2(x - 5)² is never positive. Its largest value is zero when x = 5. Therefore the maximum y-value is 35, the height of the vertex.

Scope reference: College Board’s section overview. Questions are independently authored and are not official exam material.

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