Class 10 Maths Chapter 4 Exercise 4.3 Solutions 2026 – Functions and Graphs Notes PDF

Unit 4: Functions and Graphs | Exercise 4.3 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 4.3 solutions for Functions and Graphs have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

When the Line Becomes a Curve

Linear functions always produce a straight line, but quadratic functions — anything with an x² term — produce a smooth, symmetric curve called a parabola. Exercise 4.3 applies the same table-of-values method from Exercise 4.2 to these curved graphs, while introducing a few new features unique to parabolas.

Key Concepts Covered in Exercise 4.3

Shape of a Quadratic Graph

The graph of y = ax² + bx + c is always a parabola. If a > 0, the parabola opens upward like a cup; if a < 0, it opens downward like a dome.

The Vertex

The vertex is the turning point of the parabola — its lowest point when the graph opens upward, or its highest point when it opens downward. The x-coordinate of the vertex can be found using x = −b/2a.

The Axis of Symmetry

Every parabola is a mirror image of itself across a vertical line passing through the vertex, called the axis of symmetry. Its equation is simply x = −b/2a — the same value used to find the vertex.

Building a Table of Values for a Parabola

Because the graph curves, more points are usually needed than for a straight line — typically including the vertex and two or three points on either side of it, so the symmetry of the curve is clearly visible.

Step-by-Step Solved Examples

Q. No. 1: Find the vertex of y = x² − 4x + 3.

a = 1, b = −4

x-coordinate of vertex = −b/2a = −(−4)/2(1) = 4/2 = 2

Find y at x = 2: y = (2)² − 4(2) + 3 = 4 − 8 + 3 = −1

Vertex: (2, −1)

Q. No. 2: Complete a table of values for y = x² − 4x + 3 using x = 0, 1, 2, 3, 4.

x=0: y=0−0+3=3     x=1: y=1−4+3=0

x=2: y=4−8+3=−1 (the vertex)     x=3: y=9−12+3=0

x=4: y=16−16+3=3

Table: (0,3), (1,0), (2,−1), (3,0), (4,3) — notice the symmetry around x=2

Q. No. 3: State the equation of the axis of symmetry for y = x² − 4x + 3.

Axis of symmetry: x = −b/2a = −(−4)/2(1) = 2

Equation: x = 2

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 4.3 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on whether a parabola opens upward or downward based on the sign of a
• Short Questions: Finding the vertex or axis of symmetry of a given quadratic function
• Long Questions: Full graph sketching from a table of values, including labeling the vertex

Where This Matters Beyond This Exercise

Notice that Q. No. 1’s table in this exercise produces the same y = 0 points at x = 1 and x = 3 — these are exactly the roots that Exercise 2.1 in Chapter 2 would have found by factorizing x² − 4x + 3 = 0. Graphing a quadratic function is really a visual way of finding where the related quadratic equation equals zero. Parabolas also describe real-world motion, such as the path of a thrown ball under gravity.

Common Mistakes Students Make in Exercise 4.3

• Forgetting the negative sign in −b/2a when finding the vertex
• Not choosing enough points around the vertex, resulting in a lopsided or inaccurate curve
• Connecting plotted points with straight line segments instead of a smooth curve
• Mixing up which direction the parabola opens based on the sign of a

Why This Exercise Matters for the Board Exam

Quadratic graph questions typically carry more marks than linear ones, since they require the additional vertex calculation as well as an accurate curved sketch. Clearly labeling the vertex and axis of symmetry on the final graph, not just plotting points, is often specifically required for full marks.

Quick Links – Chapter 4: Functions and Graphs

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Download Exercise 4.3 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 4.3 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. How is a quadratic graph related to Chapter 2 (Quadratic Equations)?

The points where a quadratic graph crosses the x-axis (where y = 0) are exactly the roots of the related quadratic equation, whether found by factorization, completing the square, or the quadratic formula in Chapter 2.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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