Quadratic Factored Form Math Example 2

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Example 2

medium
Write a quadratic in factored form with zeros at x=3x = 3 and x=−2x = -2 and passing through (0,−12)(0, -12).

Solution

  1. 1
    Start with f(x)=a(x−3)(x+2)f(x) = a(x - 3)(x + 2).
  2. 2
    Use (0,−12)(0, -12): −12=a(0−3)(0+2)=−6a-12 = a(0 - 3)(0 + 2) = -6a.
  3. 3
    Solve: a=2a = 2. So f(x)=2(x−3)(x+2)f(x) = 2(x - 3)(x + 2).

Answer

f(x)=2(x−3)(x+2)f(x) = 2(x - 3)(x + 2)
Given the zeros, write the general factored form and use one additional point to determine the leading coefficient aa.

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 1 easy

What are the zeros of [formula]?

Example 3 easy

Find the zeros of [formula].

Example 4 medium

Find the axis of symmetry of [formula].

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