Find The { Y $}$-intercept Of The Parabola { Y = -x^2 + 3x $} . S I M P L I F Y Y O U R A N S W E R A N D W R I T E I T A S A P R O P E R F R A C T I O N , I M P R O P E R F R A C T I O N , O R I N T E G E R . .Simplify Your Answer And Write It As A Proper Fraction, Improper Fraction, Or Integer. . S Im Pl I F Yyo U R An S W Er An D W R I T E I T A S A P Ro P Er F R A C T I O N , Im P Ro P Er F R A C T I O N , Or In T E G Er . { \square \}

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Introduction

In mathematics, the y-intercept of a parabola is the point at which the parabola intersects the y-axis. It is an essential concept in algebra and calculus, and understanding how to find the y-intercept of a parabola is crucial for solving various mathematical problems. In this article, we will focus on finding the y-intercept of the parabola y = -x^2 + 3x.

What is a Parabola?

A parabola is a type of quadratic equation that can be represented in the form y = ax^2 + bx + c, where a, b, and c are constants. The parabola can open upwards or downwards, depending on the value of a. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards.

The y-Intercept of a Parabola

The y-intercept of a parabola is the point at which the parabola intersects the y-axis. It is the value of y when x is equal to zero. To find the y-intercept of a parabola, we need to substitute x = 0 into the equation of the parabola.

Finding the y-Intercept of the Parabola y = -x^2 + 3x

To find the y-intercept of the parabola y = -x^2 + 3x, we need to substitute x = 0 into the equation. This gives us:

y = -(0)^2 + 3(0) y = 0

Therefore, the y-intercept of the parabola y = -x^2 + 3x is 0.

Simplifying the Answer

In this case, the answer is already simplified, and it is an integer. However, if the answer were a fraction or a decimal, we would need to simplify it further.

Improper Fractions and Integers

An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. An integer is a whole number that is not a fraction or a decimal. In this case, the answer is an integer, which is 0.

Conclusion

In conclusion, finding the y-intercept of a parabola is a straightforward process that involves substituting x = 0 into the equation of the parabola. In this article, we focused on finding the y-intercept of the parabola y = -x^2 + 3x, and we found that the y-intercept is 0. This is an integer, which is already simplified.

Frequently Asked Questions

Q: What is the y-intercept of a parabola?

A: The y-intercept of a parabola is the point at which the parabola intersects the y-axis.

Q: How do I find the y-intercept of a parabola?

A: To find the y-intercept of a parabola, substitute x = 0 into the equation of the parabola.

Q: What is the y-intercept of the parabola y = -x^2 + 3x?

A: The y-intercept of the parabola y = -x^2 + 3x is 0.

References

Further Reading

Related Topics

  • [1] Finding the x-Intercept of a Parabola
  • [2] Graphing a Parabola
  • [3] Solving Quadratic Equations

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Introduction

In our previous article, we discussed how to find the y-intercept of a parabola. However, we understand that there may be some questions and concerns that readers may have. In this article, we will address some of the most frequently asked questions about finding the y-intercept of a parabola.

Q&A

Q: What is the y-intercept of a parabola?

A: The y-intercept of a parabola is the point at which the parabola intersects the y-axis.

Q: How do I find the y-intercept of a parabola?

A: To find the y-intercept of a parabola, substitute x = 0 into the equation of the parabola.

Q: What is the equation of a parabola?

A: The equation of a parabola is in the form y = ax^2 + bx + c, where a, b, and c are constants.

Q: What is the significance of the y-intercept of a parabola?

A: The y-intercept of a parabola is significant because it represents the point at which the parabola intersects the y-axis. This point is also known as the origin.

Q: Can the y-intercept of a parabola be negative?

A: Yes, the y-intercept of a parabola can be negative. This occurs when the parabola opens downwards.

Q: Can the y-intercept of a parabola be a fraction?

A: Yes, the y-intercept of a parabola can be a fraction. This occurs when the parabola is not a perfect square.

Q: How do I simplify the y-intercept of a parabola?

A: To simplify the y-intercept of a parabola, you need to simplify the fraction or decimal to its simplest form.

Q: What is the difference between the y-intercept and the x-intercept of a parabola?

A: The y-intercept of a parabola is the point at which the parabola intersects the y-axis, while the x-intercept of a parabola is the point at which the parabola intersects the x-axis.

Q: Can the y-intercept of a parabola be an integer?

A: Yes, the y-intercept of a parabola can be an integer. This occurs when the parabola is a perfect square.

Q: How do I graph a parabola with a given y-intercept?

A: To graph a parabola with a given y-intercept, you need to use the equation of the parabola and the y-intercept to find the x-intercepts.

Conclusion

In conclusion, finding the y-intercept of a parabola is a straightforward process that involves substituting x = 0 into the equation of the parabola. We hope that this article has addressed some of the most frequently asked questions about finding the y-intercept of a parabola.

Frequently Asked Questions: Graphing a Parabola

Q: How do I graph a parabola?

A: To graph a parabola, you need to use the equation of the parabola and the y-intercept to find the x-intercepts.

Q: What is the significance of the x-intercepts of a parabola?

A: The x-intercepts of a parabola are significant because they represent the points at which the parabola intersects the x-axis.

Q: Can the x-intercepts of a parabola be negative?

A: Yes, the x-intercepts of a parabola can be negative.

Q: Can the x-intercepts of a parabola be a fraction?

A: Yes, the x-intercepts of a parabola can be a fraction.

Q: How do I simplify the x-intercepts of a parabola?

A: To simplify the x-intercepts of a parabola, you need to simplify the fraction or decimal to its simplest form.

References

Further Reading

Related Topics

  • [1] Finding the x-Intercept of a Parabola
  • [2] Graphing a Parabola
  • [3] Solving Quadratic Equations