Sketching Graphs & Intercepts

IGCSE Edexcel Mathematics
3.5 Graphs
& Intercepts
Reminders: For y = mx + c: the y-intercept is c; set y = 0 to find the x-intercept. For quadratics: set y = 0 to find x-intercepts (roots); set x = 0 to find the y-intercept. Sketch the correct U or ∩ shape.

Section A: Straight Line Graphs

For each equation, sketch the graph on your paper and label the x-intercept and y-intercept with their coordinates.

1. y = 2x + 4
2. y = −x + 3
3. y = 3x − 6
4. y = −2x − 4
5. y = x + 5
6. y = −3x + 9
7. y = ½x − 2
8. 2x + 3y = 12

Section B: Quadratic Graphs

Sketch the graph. Label the x-intercept(s) and y-intercept. Show clearly whether the parabola opens upward or downward.

9. y = x² − 9
10. y = x² + 2x − 3
11. y = x² − 5x + 6
12. y = −x² + 4
13. y = x² − 2x − 8
14. y = x² + 6x + 9
15. y = x² − x − 6
16. y = −x² + 3x + 4

Section C: Mixed Challenge

Sketch each graph and label all intercepts. Some may need rearranging first.

17. 3x − 2y = 6
18. y = −x² + 2x + 8
19. y − 2x = 10
20. y = x² − 4x

Mark Scheme — Key Intercepts

Section A: Straight Lines

1. y = 2x + 4  →  y-int: (0, 4)   x-int: (−2, 0)
2. y = −x + 3  →  y-int: (0, 3)   x-int: (3, 0)
3. y = 3x − 6  →  y-int: (0, −6)   x-int: (2, 0)
4. y = −2x − 4  →  y-int: (0, −4)   x-int: (−2, 0)
5. y = x + 5  →  y-int: (0, 5)   x-int: (−5, 0)
6. y = −3x + 9  →  y-int: (0, 9)   x-int: (3, 0)
7. y = ½x − 2  →  y-int: (0, −2)   x-int: (4, 0)
8. 2x + 3y = 12  →  y-int: (0, 4)   x-int: (6, 0)

Section B: Quadratics

9. y = x² − 9  →  y-int: (0, −9)   x-ints: (−3, 0) & (3, 0)
10. y = x² + 2x − 3  →  y-int: (0, −3)   x-ints: (−3, 0) & (1, 0)
11. y = x² − 5x + 6  →  y-int: (0, 6)   x-ints: (2, 0) & (3, 0)
12. y = −x² + 4  →  y-int: (0, 4)   x-ints: (−2, 0) & (2, 0) [∩ shape]
13. y = x² − 2x − 8  →  y-int: (0, −8)   x-ints: (−2, 0) & (4, 0)
14. y = x² + 6x + 9  →  y-int: (0, 9)   x-int: (−3, 0) repeated root
15. y = x² − x − 6  →  y-int: (0, −6)   x-ints: (−2, 0) & (3, 0)
16. y = −x² + 3x + 4  →  y-int: (0, 4)   x-ints: (−1, 0) & (4, 0) [∩ shape]

Section C: Mixed

17. 3x − 2y = 6  →  y-int: (0, −3)   x-int: (2, 0)
18. y = −x² + 2x + 8  →  y-int: (0, 8)   x-ints: (−2, 0) & (4, 0) [∩ shape]
19. y − 2x = 10  →  y-int: (0, 10)   x-int: (−5, 0)
20. y = x² − 4x  →  y-int: (0, 0)   x-ints: (0, 0) & (4, 0)

Visual Mark Scheme — All Questions

Every graph shows the correct shape with all intercepts labelled.