Drawing the graph of a quadratic function, reading roots, turning point and axis of symmetry from it, the completed-square form, and sketching.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Every ball thrown, every bridge arch, every profit curve is a parabola. The graph of a quadratic tells you its whole story: where it crosses, where it turns, how high it gets.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Change a, b and c and see the turning point and roots.
Copy these into your notebook in your own words — that is how they stick.
Table of values; plot points carefully; join with a smooth curve; label axes and the curve.
a > 0: ∪ minimum. a < 0: ∩ maximum.
x-intercepts: solutions of ax² + bx + c = 0.
x = −b/(2a), halfway between the roots.
On the axis of symmetry: substitute x = −b/2a to find y.
y = a(x + h)² + k → vertex (−h, k), axis x = −h.
To solve f(x) = k draw y = k and read the x-values of the intersections.
The gradient of a curve at a point is the gradient of the tangent there.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (20 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [11 marks]
The function f is defined by f(x) = x² − 2x − 3.
(a) Complete the table of values for x = −2, −1, 0, 1, 2, 3, 4. [2]
(b) Using a scale of 2 cm to 1 unit on the x-axis and 1 cm to 1 unit on the y-axis, draw the graph. (Check your drawing: labelled axes, correct scales, points plotted, smooth curve, y-intercept (0, −3), roots at −1 and 3.) [3]
(c) From the graph state (i) the roots of f(x) = 0, (ii) the equation of the axis of symmetry, (iii) the coordinates and nature of the turning point. [3]
(d) Show that the equation x² − 2x − 5 = 0 can be solved by drawing y = 2 on your graph, and read the solutions. [3]
Question 2 [9 marks]
The function g is defined by g(x) = −x² + 4x + 5.
(a) Express g(x) in the form a(x + h)² + k. [3]
(b) State the coordinates of the maximum point and the equation of the axis of symmetry. [2]
(c) Find the roots of g(x) = 0 and hence the values of x for which g(x) ≥ 0. [4]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.