Quadratic Factored Form Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
What are the zeros of f(x)=(x−1)(x+4)f(x) = (x - 1)(x + 4)?

Solution

  1. 1
    Set each factor to zero: x−1=0x - 1 = 0 gives x=1x = 1; x+4=0x + 4 = 0 gives x=−4x = -4.
  2. 2
    The zeros are x=1x = 1 and x=−4x = -4.
  3. 3
    The graph crosses the xx-axis at these points.

Answer

x=1 and x=−4x = 1 \text{ and } x = -4
In factored form a(x−r1)(x−r2)a(x - r_1)(x - r_2), the zeros are read directly as r1r_1 and r2r_2. This is the most convenient form for finding xx-intercepts.

About Quadratic Factored Form

The factored form of a quadratic function is f(x)=a(x−r1)(x−r2)f(x) = a(x - r_1)(x - r_2), where r1r_1 and r2r_2 are the zeros (roots) of the function and aa is the leading coefficient.

Learn more about Quadratic Factored Form →

More Quadratic Factored Form Examples

Example 2 medium

Write a quadratic in factored form with zeros at [formula] and [formula] and passing through [formul

Example 3 easy

Find the zeros of [formula].

Example 4 medium

Find the axis of symmetry of [formula].

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