Evaluate The Expression $y^2 - 5y + 6$ When $y = -5$.

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Introduction

In mathematics, evaluating an expression involves substituting a given value into the expression and simplifying it to obtain the final result. In this article, we will focus on evaluating the quadratic expression $y^2 - 5y + 6$ when $y = -5$. We will break down the process into manageable steps, making it easy to understand and follow along.

Understanding Quadratic Expressions

A quadratic expression is a polynomial of degree two, which means it has a highest power of two. The general form of a quadratic expression is $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. In our given expression, $y^2 - 5y + 6$, we can identify the coefficients as follows:

  • a = 1$ (coefficient of $y^2$)

  • b = -5$ (coefficient of $y$)

  • c = 6$ (constant term)

Substituting the Value of y

To evaluate the expression, we need to substitute the given value of $y$, which is $-5$, into the expression. This means we will replace every instance of $y$ with $-5$.

y2−5y+6y^2 - 5y + 6

becomes

(−5)2−5(−5)+6(-5)^2 - 5(-5) + 6

Simplifying the Expression

Now that we have substituted the value of $y$, we can simplify the expression by following the order of operations (PEMDAS):

  1. Evaluate the exponent: $(-5)^2 = 25$
  2. Multiply $-5$ and $-5$: $-5(-5) = 25$
  3. Add and subtract the terms: $25 + 25 + 6 = 56$

Final Result

After simplifying the expression, we get the final result:

5656

Conclusion

Evaluating a quadratic expression involves substituting a given value into the expression and simplifying it to obtain the final result. By following the steps outlined in this article, we can easily evaluate the expression $y^2 - 5y + 6$ when $y = -5$. The final result is $56$.

Frequently Asked Questions

Q: What is a quadratic expression?

A: A quadratic expression is a polynomial of degree two, which means it has a highest power of two.

Q: How do I evaluate a quadratic expression?

A: To evaluate a quadratic expression, substitute the given value into the expression and simplify it to obtain the final result.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions 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.

Example Problems

Problem 1: Evaluate the expression $x^2 + 3x - 4$ when $x = 2$.

Solution:

x2+3x−4x^2 + 3x - 4

becomes

22+3(2)−42^2 + 3(2) - 4

=4+6−4= 4 + 6 - 4

=6= 6

Problem 2: Evaluate the expression $y^2 - 2y + 1$ when $y = -3$.

Solution:

y2−2y+1y^2 - 2y + 1

becomes

(−3)2−2(−3)+1(-3)^2 - 2(-3) + 1

=9+6+1= 9 + 6 + 1

=16= 16

Practice Problems

Evaluate the following expressions when the given values are substituted:

  1. x^2 - 4x + 3$ when $x = 1

  2. y^2 + 2y - 5$ when $y = -2

  3. z^2 - 3z + 2$ when $z = 0

References

Further Reading

By following the steps outlined in this article, you can easily evaluate quadratic expressions and simplify them to obtain the final result. Remember to substitute the given value into the expression and simplify it using the order of operations (PEMDAS). With practice, you will become proficient in evaluating quadratic expressions and solving problems involving quadratic equations.

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Introduction

Evaluating quadratic expressions is a fundamental concept in mathematics, and it's essential to understand how to do it correctly. In this article, we will provide a comprehensive Q&A guide to help you evaluate quadratic expressions and simplify them to obtain the final result.

Q&A: Evaluating Quadratic Expressions

Q: What is a quadratic expression?

A: A quadratic expression is a polynomial of degree two, which means it has a highest power of two. It can be written in the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I evaluate a quadratic expression?

A: To evaluate a quadratic expression, substitute the given value into the expression and simplify it to obtain the final result. You can use the order of operations (PEMDAS) to simplify the expression.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions 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 a quadratic expression?

A: To simplify a quadratic expression, follow these steps:

  1. Substitute the given value into the expression.
  2. Simplify the expression using the order of operations (PEMDAS).
  3. Combine like terms to obtain the final result.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x^2$ and $5x^2$ are like terms because they both have the variable $x$ and the exponent $2$.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, $2x^2 + 5x^2 = 7x^2$.

Q: What is the final result of evaluating a quadratic expression?

A: The final result of evaluating a quadratic expression is the simplified expression after substituting the given value and combining like terms.

Q&A: Quadratic Expression Examples

Q: Evaluate the expression $x^2 + 3x - 4$ when $x = 2$.

A: To evaluate the expression, substitute $x = 2$ into the expression and simplify it using the order of operations (PEMDAS).

x2+3x−4x^2 + 3x - 4

becomes

22+3(2)−42^2 + 3(2) - 4

=4+6−4= 4 + 6 - 4

=6= 6

Q: Evaluate the expression $y^2 - 2y + 1$ when $y = -3$.

A: To evaluate the expression, substitute $y = -3$ into the expression and simplify it using the order of operations (PEMDAS).

y2−2y+1y^2 - 2y + 1

becomes

(−3)2−2(−3)+1(-3)^2 - 2(-3) + 1

=9+6+1= 9 + 6 + 1

=16= 16

Q&A: Quadratic Expression Practice

Q: Evaluate the expression $x^2 - 4x + 3$ when $x = 1$.

A: To evaluate the expression, substitute $x = 1$ into the expression and simplify it using the order of operations (PEMDAS).

x2−4x+3x^2 - 4x + 3

becomes

12−4(1)+31^2 - 4(1) + 3

=1−4+3= 1 - 4 + 3

=0= 0

Q: Evaluate the expression $y^2 + 2y - 5$ when $y = -2$.

A: To evaluate the expression, substitute $y = -2$ into the expression and simplify it using the order of operations (PEMDAS).

y2+2y−5y^2 + 2y - 5

becomes

(−2)2+2(−2)−5(-2)^2 + 2(-2) - 5

=4−4−5= 4 - 4 - 5

=−5= -5

Conclusion

Evaluating quadratic expressions is a fundamental concept in mathematics, and it's essential to understand how to do it correctly. By following the steps outlined in this article, you can easily evaluate quadratic expressions and simplify them to obtain the final result. Remember to substitute the given value into the expression and simplify it using the order of operations (PEMDAS). With practice, you will become proficient in evaluating quadratic expressions and solving problems involving quadratic equations.

Frequently Asked Questions

Q: What is a quadratic expression?

A: A quadratic expression is a polynomial of degree two, which means it has a highest power of two.

Q: How do I evaluate a quadratic expression?

A: To evaluate a quadratic expression, substitute the given value into the expression and simplify it to obtain the final result.

Q: What is the order of operations (PEMDAS)?

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

References

Further Reading

By following the steps outlined in this article, you can easily evaluate quadratic expressions and simplify them to obtain the final result. Remember to substitute the given value into the expression and simplify it using the order of operations (PEMDAS). With practice, you will become proficient in evaluating quadratic expressions and solving problems involving quadratic equations.