Which Of The Answer Choices Below Shows The Following Equation Correctly Rewritten Using The Quadratic Formula?Given Equation: X 2 − 35 X + 70 = 0 X^2 - 35x + 70 = 0 X 2 − 35 X + 70 = 0 A. X = − 35 ± ( − 35 ) 2 − 4 ( 1 ) ( 70 ) 2 ( 1 ) X = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)} X = 2 ( 1 ) − 35 ± ( − 35 ) 2 − 4 ( 1 ) ( 70 ) ​ ​ B. $x = \frac{-35 \pm

by ADMIN 360 views

Introduction

The quadratic formula is a powerful tool used to solve quadratic equations of the form ax2+bx+c=0ax^2 + bx + c = 0. It is a fundamental concept in algebra and is widely used in various fields such as physics, engineering, and economics. In this article, we will explore how to rewrite the quadratic formula using a given equation and identify the correct answer choice.

The Quadratic Formula

The quadratic formula is given by:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

where aa, bb, and cc are the coefficients of the quadratic equation.

Given Equation

The given equation is:

x2−35x+70=0x^2 - 35x + 70 = 0

We can rewrite this equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0 as:

x2−35x+70=0x^2 - 35x + 70 = 0

where a=1a = 1, b=−35b = -35, and c=70c = 70.

Rewriting the Quadratic Formula

To rewrite the quadratic formula using the given equation, we need to substitute the values of aa, bb, and cc into the formula.

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting a=1a = 1, b=−35b = -35, and c=70c = 70, we get:

x=−(−35)±(−35)2−4(1)(70)2(1)x = \frac{-(-35) \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

Simplifying the expression, we get:

x=35±1225−2802x = \frac{35 \pm \sqrt{1225 - 280}}{2}

x=35±9452x = \frac{35 \pm \sqrt{945}}{2}

x=35±31052x = \frac{35 \pm 3\sqrt{105}}{2}

Answer Choices

Now that we have rewritten the quadratic formula using the given equation, let's examine the answer choices.

A. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

B. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

C. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

D. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

Which Answer Choice is Correct?

Based on our rewritten quadratic formula, we can see that the correct answer choice is:

A. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

This answer choice correctly represents the rewritten quadratic formula using the given equation.

Conclusion

In this article, we explored how to rewrite the quadratic formula using a given equation and identified the correct answer choice. We saw that the quadratic formula is a powerful tool used to solve quadratic equations and is widely used in various fields. By following the steps outlined in this article, you can rewrite the quadratic formula using any given equation and identify the correct answer choice.

Frequently Asked Questions

Q: What is the quadratic formula?

A: The quadratic formula is a powerful tool used to solve quadratic equations of the form ax2+bx+c=0ax^2 + bx + c = 0. It is given by:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Q: How do I rewrite the quadratic formula using a given equation?

A: To rewrite the quadratic formula using a given equation, you need to substitute the values of aa, bb, and cc into the formula.

Q: What are the answer choices for the given equation?

A: The answer choices for the given equation are:

A. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

B. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

C. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

D. x=−35±(−35)2−4(1)(70)2(1)x = \frac{-35 \pm \sqrt{(-35)^2 - 4(1)(70)}}{2(1)}

Q: Which answer choice is correct?

A: The correct answer choice is:

Introduction

The quadratic formula is a powerful tool used to solve quadratic equations of the form ax2+bx+c=0ax^2 + bx + c = 0. It is a fundamental concept in algebra and is widely used in various fields such as physics, engineering, and economics. In this article, we will answer some of the most frequently asked questions about the quadratic formula.

Q: What is the quadratic formula?

A: The quadratic formula is a powerful tool used to solve quadratic equations of the form ax2+bx+c=0ax^2 + bx + c = 0. It is given by:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Q: How do I use the quadratic formula to solve a quadratic equation?

A: To use the quadratic formula to solve a quadratic equation, you need to follow these steps:

  1. Write the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0.
  2. Identify the values of aa, bb, and cc.
  3. Substitute the values of aa, bb, and cc into the quadratic formula.
  4. Simplify the expression to find the solutions.

Q: What are the steps to rewrite the quadratic formula using a given equation?

A: To rewrite the quadratic formula using a given equation, you need to follow these steps:

  1. Write the given equation in the form ax2+bx+c=0ax^2 + bx + c = 0.
  2. Identify the values of aa, bb, and cc.
  3. Substitute the values of aa, bb, and cc into the quadratic formula.
  4. Simplify the expression to find the rewritten quadratic formula.

Q: How do I identify the correct answer choice for a quadratic equation?

A: To identify the correct answer choice for a quadratic equation, you need to follow these steps:

  1. Write the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0.
  2. Identify the values of aa, bb, and cc.
  3. Substitute the values of aa, bb, and cc into the quadratic formula.
  4. Simplify the expression to find the solutions.
  5. Compare the solutions to the answer choices to identify the correct one.

Q: What are some common mistakes to avoid when using the quadratic formula?

A: Some common mistakes to avoid when using the quadratic formula include:

  • Not writing the quadratic equation in the correct form.
  • Not identifying the values of aa, bb, and cc correctly.
  • Not substituting the values of aa, bb, and cc into the quadratic formula correctly.
  • Not simplifying the expression correctly.

Q: How do I check my work when using the quadratic formula?

A: To check your work when using the quadratic formula, you need to follow these steps:

  1. Write the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0.
  2. Identify the values of aa, bb, and cc.
  3. Substitute the values of aa, bb, and cc into the quadratic formula.
  4. Simplify the expression to find the solutions.
  5. Check that the solutions satisfy the original quadratic equation.

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

A: The quadratic formula has many real-world applications, including:

  • Physics: The quadratic formula is used to solve problems involving motion, such as the trajectory of a projectile.
  • Engineering: The quadratic formula is used to design and optimize systems, such as bridges and buildings.
  • Economics: The quadratic formula is used to model and analyze economic systems, such as supply and demand.

Conclusion

In this article, we have answered some of the most frequently asked questions about the quadratic formula. We have covered topics such as how to use the quadratic formula to solve a quadratic equation, how to rewrite the quadratic formula using a given equation, and how to identify the correct answer choice. We have also discussed some common mistakes to avoid and how to check your work when using the quadratic formula.