Given that f, of, x, equals, x, squared, plus 17, x, plus, 72 and g(x)=x+8 find f(x)-g(x)

You are given the functions:

- \( f(x) = x^2 + 17x + 72 \)
- \( g(x) = x + 8 \)

To find \( f(x) - g(x) \), subtract \( g(x) \) from \( f(x) \):

\[
f(x) - g(x) = (x^2 + 17x + 72) - (x + 8)
\]

Now distribute the negative sign across \( g(x) \):

\[
f(x) - g(x) = x^2 + 17x + 72 - x - 8
\]

Combine like terms:

\[
f(x) - g(x) = x^2 + (17x - x) + (72 - 8)
\]
\[
f(x) - g(x) = x^2 + 16x + 64
\]

Thus, \( f(x) - g(x) = x^2 + 16x + 64 \).

Would you like more details or have any questions?

Here are 5 questions to deepen your understanding:
1. How would you solve for the roots of \( f(x) - g(x) = 0 \)?
2. What is the vertex of the quadratic \( f(x) - g(x) \)?
3. How would you graph \( f(x) - g(x) \)?
4. How does \( f(x) - g(x) \) change if the coefficients of \( f(x) \) are altered?
5. How would you interpret \( f(x) - g(x) \) in terms of the intersection of \( f(x) \) and \( g(x) \)?

**Tip**: Always double-check your work by combining like terms carefully when performing algebraic operations.

Given that f(x) = x^2 + 17x + 72 and g(x) = x + 8, find f(x) - g(x).

Learn how to subtract the functions f(x) = x^2 + 17x + 72 and g(x) = x + 8. This problem focuses on algebraic concepts like polynomial subtraction and simplifying quadratic expressions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation