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

User Ulaga
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1 Answer

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Answer:

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.

User Paul Alexander
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