Quadratic Expressions Practice Questions

KCSE (Kenya) · KCSE Mathematics · 145 free MCQs with instant results and detailed explanations.

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Sample Questions from Quadratic Expressions

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Easy

Which of the following represents a quadratic expression?

A. 3x^2 + 2x - 5

B. 4x + 7

C. 2x^3 - x + 1

D. 5/x + 6

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Correct Answer: A

A quadratic expression is of the form ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. Option A fits this form.

Easy

If the quadratic function f(x) = x^2 - 4x + 3 is graphed, what is the y-intercept?

A. 3

B. 0

C. -3

D. 4

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Correct Answer: A

The y-intercept of a function is found by evaluating f(0). Plugging in 0 gives f(0) = 0^2 - 4(0) + 3 = 3.

Easy

If the quadratic expression x^2 + 4x + 4 is rewritten in vertex form, what is the vertex?

A. (-2, 0)

B. (0, 4)

C. (2, 0)

D. (-4, 0)

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Correct Answer: A

The expression can be rewritten as (x + 2)^2. The vertex form indicates that the vertex is at (-2, 0).

Medium

What is the sum of the roots of the quadratic equation 2x² - 4x + 1 = 0?

A. 4

B. 2

C. 1

D. 3

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Correct Answer: B

The sum of the roots of a quadratic equation ax² + bx + c = 0 is given by -b/a. Here, a = 2 and b = -4, so the sum of the roots is -(-4)/2 = 2.

Medium

Which of the following is the vertex form of the quadratic function y = x² - 6x + 8?

A. y = (x - 3)² - 1

B. y = (x - 3)² + 1

C. y = (x + 3)² - 1

D. y = (x + 3)² + 1

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Correct Answer: A

To convert to vertex form, we complete the square: y = (x² - 6x + 9) - 1 = (x - 3)² - 1, where the vertex is (3, -1).

Medium

If the quadratic expression x² - 5x + k has roots that are both positive, what must be the value of k?

A. k < 6

B. k > 6

C. k = 6

D. k = 5

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Correct Answer: A

For the roots to be positive, the discriminant must be positive and k must be less than 6 to ensure both roots are positive based on Vieta's relations.

Medium

Which of the following quadratic equations has one repeated root?

A. x² - 4x + 4 = 0

B. x² + 2x + 3 = 0

C. 2x² - 8x + 5 = 0

D. x² - 3x + 2 = 0

Show Answer & Explanation

Correct Answer: A

A quadratic equation has one repeated root if its discriminant is zero. Here, for the equation x² - 4x + 4, the discriminant is (4)² - 4(1)(4) = 0.

Hard

If the quadratic expression x² - 6x + k can be expressed as a perfect square, what is the value of k?

A. 9

B. 16

C. 12

D. 36

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Correct Answer: A

For the expression to be a perfect square, it must be in the form (x - a)² = x² - 2ax + a². Here, -6x = -2ax gives a = 3, therefore, k must equal a² = 9.

Hard

What are the roots of the quadratic equation 2x² - 4x - 6 = 0?

A. 3 and -1

B. 1 and -3

C. 2 and -3

D. 3 and 2

Show Answer & Explanation

Correct Answer: A

Using the quadratic formula x = [-b ± √(b² - 4ac)] / 2a, where a = 2, b = -4, and c = -6, we calculate the roots as follows: b² - 4ac = (-4)² - 4(2)(-6) = 16 + 48 = 64, thus the roots are x = [4 ± 8] / 4, giving x = 3 and x = -1.

Q10

Hard

If the quadratic expression x² - 5x + k can be factored as (x - 2)(x - 3), what is the value of k?

A. 6

B. 5

C. 4

D. 3

Show Answer & Explanation

Correct Answer: A

To find k, we can expand the factored form: (x - 2)(x - 3) = x² - 5x + 6. Thus, k must equal 6 to satisfy the expression x² - 5x + k.

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Quadratic Expressions — KCSE (Kenya) KCSE Mathematics Practice Questions Online

This page contains 145 practice MCQs for the chapter Quadratic Expressions in KCSE (Kenya) KCSE Mathematics. The questions are organized by difficulty — 47 easy, 75 medium, 23 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.