5-2 Practice: Standard Form of a Quadratic Function
What is a Quadratic Function?
A quadratic function is a polynomial function of degree two, which means the highest power of the variable (usually x) is two. It has the general form:
ax^2 + bx + c = 0
where a, b, and c are constants, and a ≠ 0.
Standard Form of a Quadratic Function
The standard form of a quadratic function is written as:
ax^2 + bx + c
where a, b, and c are constants, and a ≠ 0.
Why is Standard Form Important?
The standard form of a quadratic function is important because it allows us to easily identify the key features of the function, such as the vertex, axis of symmetry, and x-intercepts. It also makes it easier to graph the function and solve quadratic equations.
Practice Exercises
Here are five practice exercises to help you master the standard form of a quadratic function:
Exercise 1
Write the quadratic function x^2 - 4x + 3 in standard form.
Answer: x^2 - 4x + 3 (already in standard form)
Exercise 2
Write the quadratic function 2x^2 + 5x - 1 in standard form.
Answer: 2x^2 + 5x - 1 (already in standard form)
Exercise 3
Write the quadratic function x^2 + 2x - 3 in standard form.
Answer: x^2 + 2x - 3 (already in standard form)
Exercise 4
Write the quadratic function -x^2 + 3x + 2 in standard form.
Answer: -x^2 + 3x + 2 (already in standard form)
Exercise 5
Write the quadratic function 4x^2 - 2x - 5 in standard form.
Answer: 4x^2 - 2x - 5 (already in standard form)
Conclusion
In this practice exercise, we learned how to identify and write quadratic functions in standard form. Remember, the standard form of a quadratic function is essential for graphing and solving quadratic equations. With practice, you'll become proficient in writing quadratic functions in standard form. Keep practicing!
