ZERO DA FUNÇÃO | RAIZ DA FUNÇÃO | AFIM ou 1º GRAU

Summary

In this educational video, Curió explains how to find the zero or root of a function step by step, using simple examples. The focus is on solving linear equations by substituting values into the function, setting the output (y or f(x)) equal to zero, and isolating the variable to find its value. Curió also covers the process of checking the solution using substitution for verification. The video reassures viewers that even with distributive functions, they can apply the same principles to solve for the root. The lesson emphasizes clarity and ease in solving for the zero of various functions.

Takeaways

• 😀 The zero of a function is the value of x that makes the function equal to zero (f(x) = 0).
• 😀 The zero of a function is also referred to as the 'root' of the function.
• 😀 To find the zero, replace f(x) with 0 and solve for x in the equation.
• 😀 In simple linear equations like f(x) = x - 3, set x - 3 = 0 to find x = 3.
• 😀 For more complex equations, rearrange the terms so that all terms involving x are on one side, and constants are on the other.
• 😀 For example, in f(x) = -3x + 12, setting f(x) = 0 gives 0 = -3x + 12, and solving gives x = 4.
• 😀 When solving, remember to isolate the variable x, performing algebraic steps like adding, subtracting, multiplying, or dividing.
• 😀 If a function has distributive properties, apply distribution first, then solve the resulting equation.
• 😀 For functions like f(x) = -2x(x + 3), distribute first to simplify the equation before solving for x.
• 😀 Always check your solution by substituting the value of x back into the original function to ensure it equals 0 (the proof of the root).
• 😀 The root or zero is where the graph of the function intersects the x-axis, and solving for it means finding this intersection point.

Q & A

What is the 'zero' or 'root' of a function?

The 'zero' or 'root' of a function is the value of 'x' that makes the function equal to zero (y = 0). This is the point where the function intersects the x-axis.

How do you find the zero of the function y = x - 3?

To find the zero of the function y = x - 3, you set y equal to zero: 0 = x - 3. Solving for x, you get x = 3, which is the root or zero of the function.

What happens when you substitute x = 3 into the function y = x - 3?

When you substitute x = 3 into the function y = x - 3, you get y = 3 - 3, which equals 0. This shows that x = 3 is indeed the zero or root of the function.

How do you solve the equation 0 = -3x + 12 to find the zero of the function?

To solve 0 = -3x + 12, move the constant term to the other side: 3x = 12. Then, divide both sides by -3, resulting in x = 4, which is the zero of the function.

What is the proof that x = 4 is the zero of the function y = -3x + 12?

To prove x = 4 is the zero, substitute x = 4 into the function y = -3x + 12: y = -3(4) + 12 = -12 + 12 = 0. This shows that when x = 4, the function equals zero.

What does it mean if someone asks for the 'root' of the function?

The 'root' of the function is the same as the 'zero' of the function. It refers to the value of x that makes the function equal to zero.

What should you do if you encounter a distributive property while finding the zero of a function?

If you encounter a distributive property while finding the zero of a function, first distribute the terms as needed, then proceed to solve the equation step by step just like a standard linear equation.

How do you solve the equation 0 = -2x(x - 3) to find the zero of the function?

First, apply the distributive property to the equation: 0 = -2x(x - 3) becomes 0 = -2x^2 + 6x. Then, solve for x by moving terms and simplifying the equation.

How do you move terms when solving an equation to find the zero of the function?

When solving to find the zero of a function, move terms involving x to one side and constants to the other side, ensuring to change the sign of terms as necessary when they cross the equals sign.

What is the final value of x when solving the equation 0 = -2x^2 + 6x?

The final value of x is 6 when solving 0 = -2x^2 + 6x, as shown by isolating x and simplifying the equation.