Maths · Rung 21 of 30

Quadratics

A parabola y = x² + bx + c crosses the x axis at its roots, where y = 0. If it factors, (x − p)(x − q) has roots p and q, with p + q = −b and p · q = c. The vertex sits halfway between the roots.

Where this sits

This is where the ladder starts: nothing is needed before it.

Exercises from this rung

Generated by the app, from easiest to hardest

  1. Where does the parabola cross the x axis?

    • 0 and 2 (1)
    • 0 and 2
    • -2 and 0
    • 1 and 2

    Why y = x² − 2x = (x − 2)(x − 0): it is 0 when x = 2 or x = 0. Check: 2 + 0 = 2 = −b and 2 × 0 = 0 = c.

    easier

  2. Where does the parabola cross the y axis?

    • 2
    • 4
    • 3
    • 1

    Why With x = 0 only the terms without x remain: y = 2. It is the marked point (0, 2).

    in between

  3. At which x is the vertex of the parabola?

    • -1.5
    • -2.5
    • 1.5
    • -0.5

    Why The vertex sits halfway between the roots -2 and -1: (-2 + -1) ÷ 2 = -1.5. Also x = −b ÷ 2a = -3 ÷ 2.

    harder