Quadratic Graphs (Edexcel IGCSE Maths)

Spec point — 3.3I

Quadratic graphs

What are the key features of a quadratic graph?

• The point where the graph turns is called the vertex

  • Positive quadratics have a minimum point

    • The bottom of the u-shape

  • Negative quadratics have a maximum point

    • The top of the n-shape

• Quadratic graphs always have a vertical line of symmetry down the middle

  • The equation of the vertical line of symmetry is x = k

    • k is the x-coordinate of the minimum or maximum point

• Quadratic graphs do not have to cross the x-axis

  • If they do, two x-intercepts are created, called roots

    • If the curve just touches the x-axis, only 1 root is created

  • Roots are symmetric about the vertical line of symmetry

• Quadratic graphs always have one y-intercept

Worked Example The graph of the equation $y=x^{2}-5x+6$ is shown below.

(a) Write down the coordinates of the roots of the equation.

Answer:

The roots of the equation are the x-intercepts of the graph

The graph crosses at x = 2 and x = 3

Final answer: The roots of the graph are at (2, 0) and (3, 0)

(b) Write down the equation of the line of symmetry.

Answer:

The line of symmetry is a vertical line that occurs halfway between the x-intercepts

Find the x-value that is halfway between the roots

The x-intercepts are x = 2 and x = 3 Halfway between is x = 2.5

Write down the equation of the line of symmetry

Final answer: x = 2.5