Math Problem Statement

Use the following function rule to find g(q–8). Simplify your answer. g(y)=y2–3y g(q–8)=

Solution

We are given the function rule:

g(y)=y23yg(y) = y^2 - 3y

To find g(q8)g(q-8), we substitute q8q-8 for yy in the expression for g(y)g(y):

g(q8)=(q8)23(q8)g(q-8) = (q-8)^2 - 3(q-8)

Now, let's simplify the expression.

  1. Expand (q8)2(q-8)^2: (q8)2=q216q+64(q-8)^2 = q^2 - 16q + 64

  2. Expand 3(q8)-3(q-8): 3(q8)=3q+24-3(q-8) = -3q + 24

Now, combine the two terms:

g(q8)=(q216q+64)3q+24g(q-8) = (q^2 - 16q + 64) - 3q + 24

  1. Simplify by combining like terms: g(q8)=q216q3q+64+24g(q-8) = q^2 - 16q - 3q + 64 + 24 g(q8)=q219q+88g(q-8) = q^2 - 19q + 88

Thus, the simplified expression for g(q8)g(q-8) is:

g(q8)=q219q+88g(q-8) = q^2 - 19q + 88


Do you need further details on how to simplify this, or have any questions?

Here are some related questions you might find interesting:

  1. How do you expand a binomial square like (q8)2(q-8)^2?
  2. How would the function change if the rule were g(y)=y2+5yg(y) = y^2 + 5y?
  3. What would happen if we wanted to find g(q+8)g(q+8) instead?
  4. Can this method be applied to higher-degree polynomials, like g(y)=y34y2+2yg(y) = y^3 - 4y^2 + 2y?
  5. How do we find the value of g(q8)g(q-8) if q=5q = 5?

Tip: When substituting into a function, always carefully expand and combine like terms to simplify your answer!

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Notation
Simplifying Expressions
Quadratic Expressions

Formulas

g(y) = y^2 - 3y

Theorems

Binomial Expansion

Suitable Grade Level

Grades 8-10