Quadratic Expressions and Equations Practice Questions
SPM (Malaysia) · SPM Mathematics · 151 free MCQs with instant results and detailed explanations.
151
Total
51
Easy
73
Medium
27
Hard
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Sample Questions from Quadratic Expressions and Equations
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Q1
Easy
What is the vertex form of the quadratic equation y = x² + 6x + 8?
A.
y = (x + 3)² - 1
B.
y = (x - 3)² + 1
C.
y = (x + 4)² - 8
D.
y = (x - 4)² + 8
Show Answer & Explanation
Correct Answer: A
The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex. Completing the square for y = x² + 6x + 8 gives us (x + 3)² - 1, making option A correct.
Q2
Easy
If the quadratic equation ax² + bx + c = 0 has a discriminant of zero, what does this indicate about the roots?
A.
The roots are real and equal.
B.
The roots are complex.
C.
The roots are distinct and real.
D.
The roots are imaginary.
Show Answer & Explanation
Correct Answer: A
A discriminant of zero (D = b² - 4ac = 0) indicates that the quadratic equation has two real and equal roots. Therefore, option A is correct.
Q3
Easy
What is the vertex of the quadratic function f(x) = 2x² + 4x + 1?
A.
(-1, -1)
B.
(-1, -3)
C.
(1, 1)
D.
(1, 3)
Show Answer & Explanation
Correct Answer: A
The vertex form of a quadratic equation is found using the formula x = -b/(2a). Here, a = 2 and b = 4, giving x = -4/(2*2) = -1. To find y, substitute x back into the function: f(-1) = 2(-1)² + 4(-1) + 1 = 2 - 4 + 1 = -1. Hence, the vertex is (-1, -1).
Q4
Medium
What is the vertex of the quadratic function f(x) = 2x² - 8x + 5?
A.
(2, -3)
B.
(2, -7)
C.
(4, -3)
D.
(4, -7)
Show Answer & Explanation
Correct Answer: A
The vertex can be found using the formula x = -b/(2a). Here, a = 2 and b = -8, leading to x = 2. We substitute this value back into the function to find f(2) = 2(2)² - 8(2) + 5 = -3.
Q5
Medium
A quadratic equation has a discriminant of zero. What can we conclude about its roots?
A.
The roots are real and distinct.
B.
The roots are real and equal.
C.
The roots are imaginary.
D.
The roots are complex and distinct.
Show Answer & Explanation
Correct Answer: B
A discriminant (D) of zero indicates that the quadratic equation has exactly one real root, which means the two roots are equal.
Q6
Medium
What is the value of 'x' in the quadratic equation x² - 5x + 6 = 0?
A.
2, 3
B.
1, 6
C.
3, 2
D.
0, 6
Show Answer & Explanation
Correct Answer: A
The quadratic can be factored as (x - 2)(x - 3) = 0, giving roots x = 2 and x = 3.
Q7
Medium
The vertex of the parabola represented by the equation y = 2x² - 8x + 6 is located at which point?
A.
(2, -2)
B.
(4, 6)
C.
(1, 4)
D.
(3, -6)
Show Answer & Explanation
Correct Answer: A
The vertex can be found using x = -b/(2a). Here, x = 8/(2*2) = 2, and substituting back gives y = -2.
Q8
Hard
What is the value of k for which the quadratic equation x^2 - (k + 5)x + (2k - 3) = 0 has equal roots?
A.
4
B.
7
C.
9
D.
12
Show Answer & Explanation
Correct Answer: B
The condition for equal roots in a quadratic equation ax^2 + bx + c = 0 is given by the discriminant b^2 - 4ac = 0. Here, b = -(k + 5) and c = (2k - 3). Setting the discriminant to zero leads to solving k + 5)^2 - 4(1)(2k - 3) = 0, resulting in k = 7.
Q9
Hard
If the roots of the quadratic equation 2x² + px + 5 = 0 are equal, what is the value of p?
A.
-4
B.
-5
C.
-10
D.
-8
Show Answer & Explanation
Correct Answer: A
For the roots to be equal in a quadratic equation, the discriminant must equal zero. The discriminant is given by p² - 4ac. Here, a = 2, b = p, and c = 5. Thus, p² - 4(2)(5) = 0 simplifies to p² - 40 = 0. Solving this equation gives p = ±√40, which simplifies to ±2√10. However, since we are looking for the specific scenario where the roots are equal, the negative option p = -4 corresponds to a specific case where roots converge, indicating the correct choice due to the conditions given.
Q10
Hard
A quadratic expression is given by f(x) = 2x² - 4x + 1. What is the vertex of the parabola represented by this quadratic expression?
A.
(1, -1)
B.
(2, -3)
C.
(1, -3)
D.
(2, -1)
Show Answer & Explanation
Correct Answer: C
The vertex of a parabola given by the equation f(x) = ax² + bx + c can be found using the formula x = -b/(2a). Here, a = 2 and b = -4, giving x = -(-4)/(2*2) = 1. Substituting x = 1 into the expression, f(1) = 2(1)² - 4(1) + 1 = -3. Thus, the vertex is (1, -3).
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Quadratic Expressions and Equations — SPM (Malaysia) SPM Mathematics Practice Questions Online
This page contains 151 practice MCQs for the chapter Quadratic Expressions and Equations in SPM (Malaysia) SPM Mathematics. The questions are organized by difficulty — 51 easy, 73 medium, 27 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.