Session 3 Check Your Understanding Sketching Quadratics

Published

September 16, 2026

Section A: Finding x- and y-intercepts of y = f(x)

For each function, find the x-intercept(s) (where y = 0) and the y-intercept (where x = 0).

  1. y = (x+3)(x+5)

  2. y = (x-2)(2x^2 + 7x + 3)

  3. y = x^2 - 4

  4. y = x^2 - 5x + 6

  5. y = 2x^2 - 8x

Section B: Sketching y = ax^2 + bx (no constant term)

For each quadratic, do the following: - Find the y-intercept. - Factorise to find the x-intercepts. - Find the vertex - State whether the parabola opens upward (a > 0) or downward (a < 0). - Sketch the graph (on paper) using this information. - label all the points clearly with both x and y coordinates.

  1. y = x^2 + 3x

  2. y = x^2 - 5x

  3. y = 2x^2 - 4x

  4. y = -x^2 + 2x

  5. y = -2x^2 - 6x

Section C: Sketching y = ax^2 + bx + c (can be factorised)

For each quadratic, do the following: - Find the y-intercept. - Factorise to find the x-intercepts. - Find the vertex - State whether the parabola opens upward (a > 0) or downward (a < 0). - Sketch the graph (on paper) using this information. - label all the points clearly with both x and y coordinates.

  1. y = x^2 + 5x + 6

  2. y = x^2 - 7x + 10

  3. y = x^2 - 2x - 8

  4. y = 2x^2 + 7x + 3

  5. y = -x^2 + x + 6