Which Of The Following Choices Lists The Correct Values Of A , H A, H A , H , And K K K For The Function F ( X ) = 5 X 2 F(x)=5x^2 F ( X ) = 5 X 2 ?A. A = 5 , H = 0 , K = 0 A=5, H=0, K=0 A = 5 , H = 0 , K = 0 B. A = 5 , H = 1 , K = 0 A=5, H=1, K=0 A = 5 , H = 1 , K = 0 C. A = 5 , H = 0 , K = 1 A=5, H=0, K=1 A = 5 , H = 0 , K = 1 D. None Of These Choices Are Correct.

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In mathematics, a quadratic function is a polynomial function of degree two, which means the highest power of the variable is two. The general form of a quadratic function is given by:

f(x) = ax^2 + bx + c

where a, b, and c are constants, and x is the variable. The quadratic function can be written in the form f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Identifying the Correct Values of a, h, and k

The given function is f(x) = 5x^2. To identify the correct values of a, h, and k, we need to rewrite the function in the form f(x) = a(x - h)^2 + k.

Step 1: Identify the Value of a

The coefficient of x^2 in the given function is 5. Therefore, the value of a is 5.

Step 2: Identify the Value of h

To identify the value of h, we need to rewrite the function in the form f(x) = a(x - h)^2 + k. Since the given function is f(x) = 5x^2, we can rewrite it as:

f(x) = 5(x - 0)^2 + 0

Comparing this with the general form f(x) = a(x - h)^2 + k, we can see that h = 0.

Step 3: Identify the Value of k

From the rewritten function f(x) = 5(x - 0)^2 + 0, we can see that k = 0.

Conclusion

Based on the analysis, the correct values of a, h, and k for the function f(x) = 5x^2 are a = 5, h = 0, and k = 0.

Answer

The correct answer is A. a=5,h=0,k=0a=5, h=0, k=0.

Discussion

The given function f(x) = 5x^2 is a quadratic function in the form f(x) = ax^2. To identify the correct values of a, h, and k, we need to rewrite the function in the form f(x) = a(x - h)^2 + k. By comparing the given function with the general form, we can see that a = 5, h = 0, and k = 0.

Example

Consider the function f(x) = 2x^2. To identify the correct values of a, h, and k, we need to rewrite the function in the form f(x) = a(x - h)^2 + k.

f(x) = 2(x - 0)^2 + 0

Comparing this with the general form f(x) = a(x - h)^2 + k, we can see that a = 2, h = 0, and k = 0.

Conclusion

In conclusion, the correct values of a, h, and k for the function f(x) = 5x^2 are a = 5, h = 0, and k = 0. This can be verified by rewriting the function in the form f(x) = a(x - h)^2 + k.

References

Keywords

  • Quadratic function
  • a, h, and k
  • Vertex of a parabola
  • Quadratic equation
  • Algebra
  • Mathematics
    Quadratic Function Q&A =========================

Q: What is a quadratic function?

A: A quadratic function is a polynomial function of degree two, which means the highest power of the variable is two. The general form of a quadratic function is given by:

f(x) = ax^2 + bx + c

where a, b, and c are constants, and x is the variable.

Q: What is the vertex of a parabola?

A: The vertex of a parabola is the point (h, k) that represents the minimum or maximum value of the quadratic function. The vertex can be found using the formula:

h = -b / 2a k = f(h)

Q: How do I rewrite a quadratic function in the form f(x) = a(x - h)^2 + k?

A: To rewrite a quadratic function in the form f(x) = a(x - h)^2 + k, you need to complete the square. This involves adding and subtracting a constant term to create a perfect square trinomial.

Q: What is the significance of the value of a in a quadratic function?

A: The value of a in a quadratic function determines the direction and width of the parabola. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The value of a also affects the width of the parabola, with larger values of a resulting in narrower parabolas.

Q: How do I find the values of h and k in a quadratic function?

A: To find the values of h and k in a quadratic function, you need to rewrite the function in the form f(x) = a(x - h)^2 + k. This involves completing the square and identifying the values of h and k from the resulting expression.

Q: What is the relationship between the vertex and the roots of a quadratic function?

A: The vertex of a quadratic function is related to the roots of the function. The x-coordinate of the vertex (h) is equal to the average of the roots, and the y-coordinate of the vertex (k) is equal to the value of the function at the average of the roots.

Q: How do I use the quadratic formula to find the roots of a quadratic function?

A: The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

This formula can be used to find the roots of a quadratic function by plugging in the values of a, b, and c.

Q: What is the significance of the discriminant in a quadratic function?

A: The discriminant is the expression b^2 - 4ac in the quadratic formula. The discriminant determines the nature of the roots of the quadratic function. If the discriminant is positive, the roots are real and distinct. If the discriminant is zero, the roots are real and equal. If the discriminant is negative, the roots are complex.

Q: How do I graph a quadratic function?

A: To graph a quadratic function, you need to identify the vertex and the direction of the parabola. You can then use this information to plot the graph of the function.

Q: What are some common applications of quadratic functions?

A: Quadratic functions have many real-world applications, including:

  • Modeling the trajectory of a projectile
  • Describing the motion of an object under the influence of gravity
  • Finding the maximum or minimum value of a function
  • Solving problems involving optimization

Conclusion

In conclusion, quadratic functions are an important concept in mathematics, with many real-world applications. By understanding the properties and behavior of quadratic functions, you can solve a wide range of problems and model complex phenomena.

References

Keywords

  • Quadratic function
  • a, h, and k
  • Vertex of a parabola
  • Quadratic equation
  • Algebra
  • Mathematics
  • Quadratic formula
  • Discriminant
  • Graphing quadratic functions
  • Applications of quadratic functions