https://file.aiquickdraw.com/mathbot/file/1727290291133rk58l5t9.jpg

The given quadratic expression is:

\[
35 - 4x + x^2
\]

We are asked to write this expression in the form \((x + a)^2 + b\), where \(a\) and \(b\) are numbers.

### Step 1: Rewrite the quadratic expression in a standard form

Let's rewrite the expression to match the standard quadratic form \(x^2 + bx + c\):
\[
x^2 - 4x + 35
\]

### Step 2: Complete the square

We will complete the square for the expression \(x^2 - 4x\). To do this, take half the coefficient of \(x\) (which is \(-4\)), square it, and add/subtract this value within the expression.

- Half of \(-4\) is \(-2\).
- Squaring \(-2\) gives \(4\).

Now, we add and subtract \(4\) inside the quadratic expression:
\[
x^2 - 4x + 4 - 4 + 35
\]
\[
= (x - 2)^2 - 4 + 35
\]
\[
= (x - 2)^2 + 31
\]

### Step 3: Final expression

Thus, the quadratic expression can be rewritten as:
\[
(x - 2)^2 + 31
\]

### Step 4: Identify \(a\) and \(b\)

By comparing \((x - 2)^2 + 31\) with \((x + a)^2 + b\), we can see that:
- \(a = -2\)
- \(b = 31\)

### Final Answer:
\[
a = -2, \quad b = 31
\]

---

Do you have any further questions, or would you like more details on this?

Here are 5 related questions to explore:

1. How do you complete the square for a general quadratic expression?
2. Can you solve quadratic equations by completing the square?
3. How would the values of \(a\) and \(b\) change if the constant term in the expression was different?
4. What is the geometric meaning of completing the square in terms of graphing parabolas?
5. How does completing the square relate to the quadratic formula?

**Tip:** Completing the square is a useful technique not just for rewriting quadratics but also for solving quadratic equations and analyzing their properties.

35 - 4x + x^2 can be written in the form (x + a)^2 + b, where a and b are numbers. Work out the values of a and b.

Learn how to rewrite the quadratic expression 35 - 4x + x^2 in the form (x + a)^2 + b by completing the square. This step-by-step solution explains key algebraic concepts for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation