Question

Find the zeros of the function. Write the smaller solution first, and the larger solution second. f(x) = (x + 4)^2 - 25.

Answer 1

The zeros of the function are x = -9 and x = 1.

Explanation:

The zeros of a function f(x) are the values of x for which f(x) = 0.

In this problem:

`f(x) = (x+4)^(2) - 25`

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = (x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\bigtriangleup))/(2*a)`

`x_(2) = (-b - √(\bigtriangleup))/(2*a)`

`\bigtriangleup = b^(2) - 4ac`

So

`f(x) = x^(2) + 8x + 16 - 25`

`f(x) = x^(2) + 8x - 9`

Zeros

`x^(2) + 8x - 9 = 0`

This means that
`a = 1, b = 8, c = -9`

`\bigtriangleup = b^(2) - 4ac = (8)^(2) - 4*1(-9) = 100`

`x_(1) = (-8 + √(100))/(2*1) = 1`

`x_(2) = (-8 - √(100))/(2*1) = -9`

The zeros of the function are x = -9 and x = 1.