Make sure to substitute the correct value of x into the equation

Oct 13, 2025 by windailys.com 127 views

Solving for y: A Step-by-Step Guide to Determining the Value of y

In mathematics, solving for a variable is a fundamental concept that is used to determine the value of a variable in an equation. In this article, we will focus on solving for y in the equation y = x^2 - 5, given that x = -3. We will break down the problem into smaller steps and provide a clear explanation of each step.

The equation y = x^2 - 5 is a quadratic equation, which means that it has a squared variable (x^2) as the main term. The equation is in the form of y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = 1, b = 0, and c = -5.

Substituting x = -3 into the Equation

To solve for y, we need to substitute x = -3 into the equation y = x^2 - 5. This means that we will replace x with -3 in the equation.

y = (-3)^2 - 5

Now that we have substituted x = -3 into the equation, we can simplify it by evaluating the expression (-3)^2. The expression (-3)^2 means that we need to multiply -3 by itself.

(-3)^2 = (-3) × (-3) = 9

So, the equation becomes:

y = 9 - 5

Now that we have simplified the equation, we can evaluate the expression 9 - 5. This means that we need to subtract 5 from 9.

9 - 5 = 4

Therefore, the value of y is 4, when x = -3.

Solving for y in the equation y = x^2 - 5 is an important concept in mathematics because it helps us to understand how to work with quadratic equations. Quadratic equations are used to model real-world problems, such as the motion of objects, the growth of populations, and the behavior of electrical circuits. By being able to solve for y in a quadratic equation, we can gain a deeper understanding of these problems and make predictions about their behavior.

The concept of solving for y in a quadratic equation has many real-world applications. For example:

Physics: Quadratic equations are used to model the motion of objects, such as the trajectory of a projectile or the motion of a pendulum.
Biology: Quadratic equations are used to model the growth of populations, such as the growth of a bacteria culture or the spread of a disease.
Engineering: Quadratic equations are used to model the behavior of electrical circuits, such as the voltage and current in a circuit.

Here are some tips and tricks for solving for y in a quadratic equation:

Make sure to substitute the correct value of x into the equation.
Simplify the equation by evaluating any expressions.
Use the order of operations to evaluate the expression.
Check your work by plugging the value of y back into the equation.

In conclusion, solving for y in the equation y = x^2 - 5 is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article, we can determine the value of y when x = -3. We hope that this article has provided a clear and concise explanation of how to solve for y in a quadratic equation.
Solving for y: A Q&A Guide to Determining the Value of y

In our previous article, we discussed how to solve for y in the equation y = x^2 - 5, given that x = -3. In this article, we will provide a Q&A guide to help you understand the concept of solving for y in a quadratic equation.

Q: What is a quadratic equation?

A: A quadratic equation is a type of equation that has a squared variable (x^2) as the main term. It is in the form of y = ax^2 + bx + c, where a, b, and c are constants.

Q: How do I know if an equation is a quadratic equation?

A: To determine if an equation is a quadratic equation, look for the squared variable (x^2). If it is present, then the equation is a quadratic equation.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:

Parentheses: Evaluate any expressions inside parentheses first.
Exponents: Evaluate any exponents (such as squaring or cubing) next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression?

A: To simplify an expression, follow these steps:

Evaluate any expressions inside parentheses.
Evaluate any exponents (such as squaring or cubing).
Perform any multiplication and division operations from left to right.
Finally, perform any addition and subtraction operations from left to right.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I solve for y in a quadratic equation?

A: To solve for y in a quadratic equation, follow these steps:

Substitute the value of x into the equation.
Simplify the equation by evaluating any expressions.
Use the order of operations to evaluate the expression.
Check your work by plugging the value of y back into the equation.

Q: What are some real-world applications of quadratic equations?

A: Quadratic equations have many real-world applications, including:

Physics: Quadratic equations are used to model the motion of objects, such as the trajectory of a projectile or the motion of a pendulum.
Biology: Quadratic equations are used to model the growth of populations, such as the growth of a bacteria culture or the spread of a disease.
Engineering: Quadratic equations are used to model the behavior of electrical circuits, such as the voltage and current in a circuit.

Q: What are some common mistakes to avoid when solving for y in a quadratic equation?

A: Some common mistakes to avoid when solving for y in a quadratic equation include:

Not substituting the correct value of x into the equation.
Not simplifying the equation by evaluating any expressions.
Not using the order of operations to evaluate the expression.
Not checking your work by plugging the value of y back into the equation.

In conclusion, solving for y in a quadratic equation is a fundamental concept in mathematics that has many real-world applications. By following the steps outlined in this article, you can determine the value of y in a quadratic equation. We hope that this article has provided a clear and concise explanation of how to solve for y in a quadratic equation.