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

B or #2). It does because 16=10+6, and the model shows 3 groups of 10 and 3 groups of 6....

Find the zeros of the function. Write the smaller

andrespacheco5888

25.01.2022

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

Step-by-step 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:

$ax^{2} + bx + c, a\neq0$ .

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:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

$f(x) = x^{2} + 8x + 16 - 25$

$f(x) = x^{2} + 8x - 9$

Zeros

$x^{2} + 8x - 9 = 0$

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

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

$x_{1} = \frac{-8 + \sqrt{100}}{2*1} = 1$

$x_{2} = \frac{-8 - \sqrt{100}}{2*1} = -9$

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

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