Use The Quadratic Model $y = -4x^2 - 3x + 4$ To Predict $y$ If $x$ Equals 5.A. -411 B. -111 C. -89 D. -51

Understanding Quadratic Equations

A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. It is often written in the form of $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. In this article, we will use the quadratic model $y = -4x^2 - 3x + 4$ to predict the value of $y$ when $x$ equals 5.

The Quadratic Model

The quadratic model $y = -4x^2 - 3x + 4$ is a specific type of quadratic equation. In this equation, the coefficient of $x^2$ is $-4$, the coefficient of $x$ is $-3$, and the constant term is $4$. To predict the value of $y$ when $x$ equals 5, we need to substitute $x = 5$ into the equation and solve for $y$.

Substituting x = 5 into the Equation

To substitute $x = 5$ into the equation, we need to replace every instance of $x$ with 5. This gives us:

$$y = -4(5)^2 - 3(5) + 4$$

Simplifying the Equation

To simplify the equation, we need to evaluate the expressions inside the parentheses. This gives us:

$$y = -4(25) - 15 + 4$$

Evaluating the Expressions

To evaluate the expressions, we need to multiply and add the numbers. This gives us:

$$y = -100 - 15 + 4$$

Simplifying Further

To simplify further, we need to combine the constants. This gives us:

$$y = -111$$

Conclusion

In this article, we used the quadratic model $y = -4x^2 - 3x + 4$ to predict the value of $y$ when $x$ equals 5. By substituting $x = 5$ into the equation and simplifying, we found that $y = -111$. This is the correct answer.

Answer

The correct answer is B. -111.

Why is this Important?

Understanding quadratic equations and how to use them to predict values is an important skill in mathematics. It has many real-world applications, such as modeling population growth, predicting stock prices, and designing electrical circuits.

Real-World Applications

Quadratic equations have many real-world applications. Some examples include:

• Population Growth: Quadratic equations can be used to model population growth and predict future population sizes.
• Stock Prices: Quadratic equations can be used to predict stock prices and make informed investment decisions.
• Electrical Circuits: Quadratic equations can be used to design electrical circuits and predict their behavior.

Conclusion

In conclusion, quadratic equations are an important part of mathematics and have many real-world applications. By understanding how to use quadratic equations to predict values, we can make informed decisions and solve complex problems.

Final Thoughts

Quadratic equations are a powerful tool for predicting values and solving complex problems. By understanding how to use them, we can make informed decisions and achieve our goals.

References

• "Quadratic Equations" by Math Open Reference
• "Quadratic Equations" by Khan Academy

Additional Resources

• Quadratic Equations Calculator: A calculator that can be used to solve quadratic equations.
• Quadratic Equations Solver: A solver that can be used to solve quadratic equations.
• Quadratic Equations Tutorial: A tutorial that provides a step-by-step guide to solving quadratic equations.
  Quadratic Equations Q&A ==========================

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about quadratic equations.

Q: What is a quadratic equation?

A: A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. It is often written in the form of $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. You can also use factoring, completing the square, or graphing to solve a quadratic equation.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that can be used to solve quadratic equations. It is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Q: How do I use the quadratic formula?

A: To use the quadratic formula, you need to plug in the values of $a$, $b$, and $c$ into the formula. Then, you can simplify the expression and solve for $x$.

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

A: A quadratic equation is a polynomial equation of degree two, while a linear equation is a polynomial equation of degree one. In other words, a quadratic equation has a squared variable, while a linear equation does not.

Q: Can I use a calculator to solve a quadratic equation?

A: Yes, you can use a calculator to solve a quadratic equation. Many calculators have a built-in quadratic equation solver that can be used to solve quadratic equations.

Q: How do I graph a quadratic equation?

A: To graph a quadratic equation, you can use a graphing calculator or a graphing software. You can also use a piece of graph paper and a pencil to graph a quadratic equation.

Q: What is the vertex of a quadratic equation?

A: The vertex of a quadratic equation is the point on the graph of the equation where the parabola changes direction. It is also the minimum or maximum point of the parabola.

Q: How do I find the vertex of a quadratic equation?

A: To find the vertex of a quadratic equation, you can use the formula: $x = \frac{-b}{2a}$. You can also use a graphing calculator or a graphing software to find the vertex.

Q: What is the axis of symmetry of a quadratic equation?

A: The axis of symmetry of a quadratic equation is a vertical line that passes through the vertex of the parabola. It is also the line of symmetry of the parabola.

Q: How do I find the axis of symmetry of a quadratic equation?

A: To find the axis of symmetry of a quadratic equation, you can use the formula: $x = \frac{-b}{2a}$. You can also use a graphing calculator or a graphing software to find the axis of symmetry.

Conclusion

In conclusion, quadratic equations are an important part of mathematics and have many real-world applications. By understanding how to solve quadratic equations, you can make informed decisions and solve complex problems.

Additional Resources

• Quadratic Equations Calculator: A calculator that can be used to solve quadratic equations.
• Quadratic Equations Solver: A solver that can be used to solve quadratic equations.
• Quadratic Equations Tutorial: A tutorial that provides a step-by-step guide to solving quadratic equations.

References

• "Quadratic Equations" by Math Open Reference
• "Quadratic Equations" by Khan Academy

Final Thoughts

Quadratic equations are a powerful tool for solving complex problems. By understanding how to solve quadratic equations, you can make informed decisions and achieve your goals.