Find Coefficients in the Equation y=3-x-x²: Step-by-Step Guide

Q: Why can't I just read the coefficients from left to right?

Coefficients must be identified from the standard form $ ax^2 + bx + c $. The original equation $ y = 3 - x - x^2 $ isn't in standard order, so you need to rearrange it first!

Q: How do I rearrange the equation correctly?

Start with $ y = 3 - x - x^2 $ and rewrite in descending powers: highest degree first. This gives you $ y = -x^2 - x + 3 $.

Q: How do I remember which coefficient is which?

Use the pattern $ ax^2 + bx + c $: a = coefficient of $ x^2 $b = coefficient of $ x $c = constant term (no variable)

Q: What if there's no x term or constant term?

If a term is missing, its coefficient is 0. For example, $ y = 2x^2 + 5 $ has $ a = 2 $, $ b = 0 $, $ c = 5 $.

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

$y=3-x-x^2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find the numbers in front of the terms in the function.

00:11 We use a formula to show a quadratic equation.

00:17 First, arrange your equation so it looks like the formula.

00:39 Next, separate the variables from the numbers in front.

00:52 Now compare your equation to the formula and find the numbers, called coefficients.

01:01 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Identify the coefficients based on the following equation

$y=3-x-x^2$

Step-by-step solution

To solve this problem, we need to compare the given quadratic function with the standard form.

The given function is $y = 3 - x - x^2$ . We can rearrange this into the standard quadratic form:

$y = -x^2 - x + 3$ .

In the standard quadratic form, $y = ax^2 + bx + c$ , we identify the coefficients:

The coefficient of $x^2$ is $a = -1$ .
The coefficient of $x$ is $b = -1$ .
The constant term is $c = 3$ .

Therefore, based on the standard quadratic form, the parameters are $a = -1$ , $b = -1$ , and $c = 3$ .

We match these coefficients to the given multiple-choice answers.

Therefore, the correct answer choice is:
$a = -1, b = -1, c = 3$ .

Final Answer

$a=-1,b=-1,c=3$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Always write quadratic equations as $ax^2 + bx + c$
Rearrange: Change $3 - x - x^2$ to $-x^2 - x + 3$
Check: Verify coefficients: $a = -1$ , $b = -1$ , $c = 3$ ✓

Common Mistakes

Avoid these frequent errors

Reading coefficients from original order
Don't read coefficients directly from $y = 3 - x - x^2$ as a = 3, b = -1, c = -1! This ignores the standard form requirement and gives wrong coefficient assignments. Always rearrange to $ax^2 + bx + c$ first, then identify coefficients.

Practice Quiz

Test your knowledge with interactive questions

What is the value of the coefficient $$ b $$ in the equation below?

$$ 3x^2+8x-5 $$

FAQ

Everything you need to know about this question

Why can't I just read the coefficients from left to right?

Coefficients must be identified from the standard form $ax^2 + bx + c$ . The original equation $y = 3 - x - x^2$ isn't in standard order, so you need to rearrange it first!

How do I rearrange the equation correctly?

Start with $y = 3 - x - x^2$ and rewrite in descending powers: highest degree first. This gives you $y = -x^2 - x + 3$ .

What if the x² term is negative like in this problem?

That's perfectly normal! The coefficient a can be positive or negative. Here, $a = -1$ because we have $-x^2$ , which means $-1 \cdot x^2$ .

How do I remember which coefficient is which?

Use the pattern $ax^2 + bx + c$ :

a = coefficient of $x^2$
b = coefficient of $x$
c = constant term (no variable)

What if there's no x term or constant term?

If a term is missing, its coefficient is 0. For example, $y = 2x^2 + 5$ has $a = 2$ , $b = 0$ , $c = 5$ .

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Find Coefficients in the Equation y=3-x-x²: Step-by-Step Guide

Quadratic Coefficients with Standard Form

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just read the coefficients from left to right?

How do I rearrange the equation correctly?

What if the x² term is negative like in this problem?

How do I remember which coefficient is which?

What if there's no x term or constant term?

🌟 Unlock Your Math Potential

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