Math Problem Statement

Complete the square for quadratic expressions in Exercise 2.7A, including questions where you rewrite quadratic expressions into completed square form.

Solution

The task in Exercise 2.7A involves expressing quadratic expressions in "completed square form." Let's start by breaking down how to approach these problems step by step.

In general, completing the square involves transforming a quadratic expression of the form:

ax2+bx+cax^2 + bx + c

into the completed square form:

a(xh)2+ka(x - h)^2 + k

where hh and kk are constants.

For Questions 1 to 12:

The task here is to rewrite the given expressions, which are already in the form of (x+p)2+q(x + p)^2 + q or (xp)2+q(x - p)^2 + q, back into the standard quadratic form ax2+bx+cax^2 + bx + c.

Would you like me to help with specific examples, or go through how to approach some of these problems, like the more complex ones in the second part of the exercise (Questions 13 to 32)?

Feel free to let me know which question you'd like to explore in more detail!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Completing the Square

Formulas

Quadratic equation: ax^2 + bx + c = 0
Completed square form: a(x - h)^2 + k

Theorems

Completing the Square Theorem

Suitable Grade Level

Grades 8-10