Find Coefficients in y=-5x²: Quadratic Equation Analysis

Q: Why is b = 0 if there's no x term in the equation?

When a term is missing from an equation, it means its coefficient is 0. Since $ y = -5x^2 $ has no x term, we can write it as $ y = -5x^2 + 0x + 0 $, so b = 0.

Q: How do I remember which coefficient is a, b, or c?

Use the alphabetical order trick: a goes with $ x^2 $ (highest power), b goes with $ x $ (middle power), and c is the constant (no x at all).

Q: What if the equation is written differently, like x² - 5 = y?

Always rearrange to standard form first! Move everything to get $ y = x^2 - 5 $, then identify: a = 1, b = 0, c = -5.

Q: Can coefficients be negative numbers?

Absolutely! Coefficients can be positive, negative, or zero. In $ y = -5x^2 $, the coefficient a = -5 is negative, which means the parabola opens downward.

Q: What's the difference between y = -5x² and y = (-5x)²?

These are completely different! $ y = -5x^2 $ means multiply x² by -5, while $ y = (-5x)^2 $ means square the entire expression -5x, giving you $ y = 25x^2 $.

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

$y=-5x^2$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the function's coefficients

00:03 We'll use the formula to represent a quadratic equation

00:12 We'll arrange the equation to match the formula

00:27 We'll separate the unknown from the coefficient

00:39 We'll compare the formula to our equation and find the coefficients

00:50 And this is the solution to the question

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

$y=-5x^2$

Step-by-step solution

To solve the problem, we'll identify the parameters $a$ , $b$ , and $c$ from the given quadratic function:

**Step 1**: Compare the given equation $y = -5x^2$ with the general quadratic form $y = ax^2 + bx + c$ .
**Step 2**: Note that the coefficient of $x^2$ is $-5$ , hence $a = -5$ .
**Step 3**: Since there is no $x$ term, $b = 0$ .
**Step 4**: Since there is no constant term, $c = 0$ .

After identifying the parameters, we conclude:

The parameters for the quadratic function are $a = -5$ , $b = 0$ , $c = 0$ . Therefore, the correct choice is:

The correct answer is $a = -5, b = 0, c = 0$ .

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic functions follow the pattern $y = ax^2 + bx + c$
Coefficient Matching: Compare $y = -5x^2$ to find a = -5, b = 0, c = 0
Verification: Check that missing terms have coefficient 0: no x term means b = 0 ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient positions or ignoring missing terms
Don't assign -5 to the wrong coefficient or forget that missing terms = coefficient of 0! This leads to answers like a=0, c=-5. Always match each coefficient to its corresponding term in standard form ax² + bx + c.

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 b = 0 if there's no x term in the equation?

When a term is missing from an equation, it means its coefficient is 0. Since $y = -5x^2$ has no x term, we can write it as $y = -5x^2 + 0x + 0$ , so b = 0.

How do I remember which coefficient is a, b, or c?

Use the alphabetical order trick: a goes with $x^2$ (highest power), b goes with $x$ (middle power), and c is the constant (no x at all).

What if the equation is written differently, like x² - 5 = y?

Always rearrange to standard form first! Move everything to get $y = x^2 - 5$ , then identify: a = 1, b = 0, c = -5.

Can coefficients be negative numbers?

Absolutely! Coefficients can be positive, negative, or zero. In $y = -5x^2$ , the coefficient a = -5 is negative, which means the parabola opens downward.

What's the difference between y = -5x² and y = (-5x)²?

These are completely different! $y = -5x^2$ means multiply x² by -5, while $y = (-5x)^2$ means square the entire expression -5x, giving you $y = 25x^2$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Find Coefficients in y=-5x²: Quadratic Equation Analysis

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 b = 0 if there's no x term in the equation?

How do I remember which coefficient is a, b, or c?

What if the equation is written differently, like x² - 5 = y?

Can coefficients be negative numbers?

What's the difference between y = -5x² and y = (-5x)²?

🌟 Unlock Your Math Potential

More Questions

The function y=ax²+bx+c

Find Coefficients in y = 4 + 3x² - x: Term-by-Term Analysis

Find Coefficients in y=3+3x²-4x: Term-by-Term Analysis

Identify Coefficients in y=-3x²-4: Quadratic Function Analysis

Identify Coefficients in the Equation 6=6x+2x²: Term Analysis

Plotting Functions with Parameters

Find Coefficients in y=6+3x: Linear Equation Analysis

Find Coefficients in y = 3x² + 4 - 5x: Term-by-Term Analysis

Identify Coefficients in y = -4x² + 3: Quadratic Equation Analysis

Find Coefficients in y = 6x - 6x² + 3: Identifying a, b, and c