Find Coefficients in the Equation y=-5x² + x: Step-by-Step Guide

Q: What if the equation is written in a different order?

The order doesn't matter! Whether it's $ y = -5x^2 + x $ or $ y = x - 5x^2 $, just match each term with $ ax^2 $, $ bx $, and $ c $.

Q: Can coefficients be negative numbers?

Absolutely! Coefficients can be positive, negative, zero, or even fractions. In this problem, $ a = -5 $ is negative, which just means the parabola opens downward.

Q: How can I double-check my coefficients?

Substitute your coefficients back: $ a = -5, b = 1, c = 0 $ gives $ y = -5x^2 + 1x + 0 = -5x^2 + x $. If it matches the original equation, you're correct!

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

$y=-5x^2+x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the function coefficients.

00:08 Use the formula A times X squared plus B times X plus C equals zero for a quadratic equation.

00:17 Now, arrange your equation to match this formula.

00:33 Separate the variable, X, from its coefficients like A, B, and C.

00:46 Compare the standard formula with your equation to identify the coefficients.

00:56 And that's how we solve the 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

$y=-5x^2+x$

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Write down the provided quadratic function and the standard form for comparison.
Step 2: Identify the coefficients $a$ , $b$ , and $c$ by matching terms.
Step 3: Match the identified coefficients with the given answer choices.

Step 1: The given quadratic function is $y = -5x^2 + x$ , and we will compare it to the standard quadratic form $y = ax^2 + bx + c$ .

Step 2: By comparing the terms, we identify:

$a = -5$ from the coefficient of $x^2$
$b = 1$ from the coefficient of $x$
$c = 0$ since there is no constant term present

Therefore, from the given choices, the correct parameter set is identified as $a = -5$ , $b = 1$ , and $c = 0$ .

Thus, the correct answer is:

$a=-5,b=1,c=0$

Final Answer

$a=-5,b=1,c=0$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Compare $y = ax^2 + bx + c$ to identify coefficients
Term Matching: $-5x^2$ gives $a = -5$ , $x$ gives $b = 1$
Check Missing Terms: No constant term means $c = 0$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting coefficient of x when no number is written
Don't assume x has no coefficient = missing the b value! When you see just x (not 0x), it means the coefficient is 1. Always remember that x means 1x, so b = 1.

Practice Quiz

Test your knowledge with interactive questions

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

$$ 4x^2+9x-2 $$

FAQ

Everything you need to know about this question

Why is the coefficient of x equal to 1 when I don't see a number?

When you see just x without a number in front, it's actually 1x! The coefficient 1 is implied but not written. It's like saying "one apple" instead of just "apple."

How do I know c = 0 if there's no constant term?

If there's no constant number at the end of the equation, then c = 0. Think of it as $y = -5x^2 + x + 0$ - the zero is just not written!

What if the equation is written in a different order?

The order doesn't matter! Whether it's $y = -5x^2 + x$ or $y = x - 5x^2$ , just match each term with $ax^2$ , $bx$ , and $c$ .

Can coefficients be negative numbers?

Absolutely! Coefficients can be positive, negative, zero, or even fractions. In this problem, $a = -5$ is negative, which just means the parabola opens downward.

How can I double-check my coefficients?

Substitute your coefficients back: $a = -5, b = 1, c = 0$ gives $y = -5x^2 + 1x + 0 = -5x^2 + x$ . If it matches the original equation, you're correct!

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Find Coefficients in the Equation y=-5x² + x: 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 is the coefficient of x equal to 1 when I don't see a number?

How do I know c = 0 if there's no constant term?

What if the equation is written in a different order?

Can coefficients be negative numbers?

How can I double-check my coefficients?

🌟 Unlock Your Math Potential

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