Quadratic Functions Math Example 5

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

Example 5

medium
Find the zeros of f(x)=x2βˆ’4xβˆ’5f(x) = x^2 - 4x - 5.

Solution

  1. 1
    Factor: (xβˆ’5)(x+1)=0(x - 5)(x + 1) = 0.
  2. 2
    Set each factor to zero: x=5x = 5 or x=βˆ’1x = -1.

Answer

x=5Β orΒ x=βˆ’1x = 5 \text{ or } x = -1
The zeros of a quadratic function are the xx-values where f(x)=0f(x) = 0. Factor and apply the zero product property.

About Quadratic Functions

A quadratic function is a polynomial function of degree 2, written as f(x)=ax2+bx+cf(x) = ax^2 + bx + c with a≠0a \neq 0, whose graph is a U-shaped curve called a parabola that opens upward when a>0a > 0 or downward when a<0a < 0.

Learn more about Quadratic Functions β†’

More Quadratic Functions Examples

Example 1 easy

Find the vertex of [formula].

Example 2 medium

Does the parabola [formula] open upward or downward? Find its maximum value.

Example 3 medium

Find the vertex and axis of symmetry of [formula].

Example 4 easy

Find the [formula]-intercept of [formula].

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