Multiply:$\[ -7.6q(q - 2.8) = \\]

Understanding the Problem

Multiplying and simplifying quadratic expressions is a fundamental concept in algebra. It involves multiplying two or more quadratic expressions together and simplifying the resulting expression. In this article, we will focus on multiplying and simplifying the quadratic expression $-7.6q(q - 2.8)$.

The Quadratic Expression

The given quadratic expression is $-7.6q(q - 2.8)$. This expression can be expanded using the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Expanding the Quadratic Expression

To expand the quadratic expression, we need to multiply the two binomials $q$ and $(q - 2.8)$.

-7.6q(q - 2.8) = -7.6q^2 + 23.52q

Simplifying the Expression

The expanded expression $-7.6q^2 + 23.52q$ can be simplified by combining like terms. In this case, there are no like terms to combine, so the expression is already simplified.

Simplified Expression

The simplified expression is $-7.6q^2 + 23.52q$.

Graphing the Expression

To graph the expression $-7.6q^2 + 23.52q$, we need to find the x-intercepts and the vertex of the parabola.

Finding the X-Intercepts

To find the x-intercepts, we need to set the expression equal to zero and solve for $q$.

-7.6q^2 + 23.52q = 0

Factoring out $q$, we get:

q(-7.6q + 23.52) = 0

This gives us two possible solutions: $q = 0$ and $-7.6q + 23.52 = 0$.

Solving for $q$ in the second equation, we get:

-7.6q = -23.52
q = 3.1

Finding the Vertex

To find the vertex, we need to use the formula $x = -\frac{b}{2a}$, where $a$ and $b$ are the coefficients of the quadratic expression.

In this case, $a = -7.6$ and $b = 23.52$. Plugging these values into the formula, we get:

x = -\frac{23.52}{2(-7.6)}
x = 1.55

Graphing the Parabola

Using the x-intercepts and the vertex, we can graph the parabola.

Conclusion

Multiplying and simplifying quadratic expressions is a fundamental concept in algebra. In this article, we focused on multiplying and simplifying the quadratic expression $-7.6q(q - 2.8)$. We expanded the expression using the distributive property, simplified the expression by combining like terms, and graphed the parabola using the x-intercepts and the vertex.

Key Takeaways

• Multiplying and simplifying quadratic expressions is a fundamental concept in algebra.
• The distributive property can be used to expand quadratic expressions.
• Like terms can be combined to simplify quadratic expressions.
• The x-intercepts and the vertex can be used to graph quadratic expressions.

Further Reading

For further reading on multiplying and simplifying quadratic expressions, we recommend the following resources:

• Algebra I: Quadratic Expressions
• Multiplying and Simplifying Quadratic Expressions

References

• Algebra I: Quadratic Expressions
• Multiplying and Simplifying Quadratic Expressions
  Multiplying and Simplifying Quadratic Expressions: Q&A =====================================================

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about multiplying and simplifying quadratic expressions.

Q: What is a quadratic expression?

A: A quadratic expression is a polynomial expression of degree two, which means it has a highest power of two. For example, $x^2 + 3x - 4$ is a quadratic expression.

Q: How do I multiply two quadratic expressions together?

A: To multiply two quadratic expressions together, you can use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. You can also use the FOIL method, which stands for First, Outer, Inner, Last.

Q: What is the FOIL method?

A: The FOIL method is a technique for multiplying two binomials together. It stands for First, Outer, Inner, Last, and it involves multiplying the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

Q: How do I simplify a quadratic expression?

A: To simplify a quadratic expression, you can combine like terms. Like terms are terms that have the same variable and exponent. For example, $2x^2 + 3x^2$ can be simplified to $5x^2$.

Q: What is the difference between a quadratic expression and a quadratic equation?

A: A quadratic expression is a polynomial expression of degree two, while a quadratic equation is an equation that can be written in the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

Q: How do I graph a quadratic expression?

A: To graph a quadratic expression, you can use the x-intercepts and the vertex. The x-intercepts are the points where the graph crosses the x-axis, and the vertex is the highest or lowest point on the graph.

Q: What is the vertex of a quadratic expression?

A: The vertex of a quadratic expression is the highest or lowest point on the graph. It can be found using the formula $x = -\frac{b}{2a}$, where $a$ and $b$ are the coefficients of the quadratic expression.

Q: How do I find the x-intercepts of a quadratic expression?

A: To find the x-intercepts of a quadratic expression, you can set the expression equal to zero and solve for $x$. This will give you the points where the graph crosses the x-axis.

Q: What is the difference between a quadratic expression and a polynomial expression?

A: A quadratic expression is a polynomial expression of degree two, while a polynomial expression is a general term that refers to any expression that can be written as a sum of terms, each of which is a product of variables and constants.

Q: How do I determine the degree of a quadratic expression?

A: To determine the degree of a quadratic expression, you can look at the highest power of the variable. In a quadratic expression, the highest power is always two.

Q: What is the coefficient of a quadratic expression?

A: The coefficient of a quadratic expression is the number that is multiplied by the variable. For example, in the expression $2x^2 + 3x - 4$, the coefficient of $x^2$ is 2, and the coefficient of $x$ is 3.

Q: How do I factor a quadratic expression?

A: To factor a quadratic expression, you can look for two numbers whose product is the constant term and whose sum is the coefficient of the linear term. These numbers can be used to write the quadratic expression as a product of two binomials.

Conclusion

Multiplying and simplifying quadratic expressions is a fundamental concept in algebra. In this article, we answered some of the most frequently asked questions about quadratic expressions, including how to multiply and simplify them, how to graph them, and how to determine their degree and coefficients.

Key Takeaways

• A quadratic expression is a polynomial expression of degree two.
• The distributive property can be used to multiply two quadratic expressions together.
• Like terms can be combined to simplify quadratic expressions.
• The x-intercepts and the vertex can be used to graph quadratic expressions.
• The degree of a quadratic expression is determined by the highest power of the variable.
• The coefficient of a quadratic expression is the number that is multiplied by the variable.

Further Reading

For further reading on quadratic expressions, we recommend the following resources:

• Algebra I: Quadratic Expressions
• Multiplying and Simplifying Quadratic Expressions

References

• Algebra I: Quadratic Expressions
• Multiplying and Simplifying Quadratic Expressions