Find the Coefficients in y=-2x²+3x+10: Quadratic Equation Analysis

Q: Why is the coefficient of x² negative in this equation?

The coefficient a = -2 includes the negative sign! This means the parabola opens downward instead of upward. Always include signs when identifying coefficients.

Q: What's the difference between a, b, and c coefficients?

a is the coefficient of $ x^2 $ (determines parabola shape), b is the coefficient of $ x $ (affects vertex position), and c is the constant term (y-intercept value).

Q: What if there's no x term in the equation?

If there's no $ x $ term visible, then b = 0. For example, in $ y = 3x^2 + 5 $, we have a = 3, b = 0, c = 5.

Q: Do I always write coefficients in a, b, c order?

Yes! Always match the standard form $ ax^2 + bx + c $. Even if the equation is rearranged, identify coefficients based on which term they belong to, not their position.

Q: Can coefficients be fractions or decimals?

Absolutely! Coefficients can be any real numbers - positive, negative, fractions, or decimals. The key is correctly identifying which number goes with which term.

Quadratic Coefficients with Standard Form

Identify the coefficients based on the following equation

$y=-2x^2+3x+10$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the function coefficients

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

00:17 We'll separate the variable from the coefficient

00:31 We'll compare the formula with our equation and find the coefficients

00:41 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

$y=-2x^2+3x+10$

Step-by-step solution

Let's determine the coefficients for the quadratic function given by $y = -2x^2 + 3x + 10$ .

Step 1: Identify $a$ .
The coefficient of $x^2$ is $-2$ . Thus, $a = -2$ .
Step 2: Identify $b$ .
The coefficient of $x$ is $3$ . Thus, $b = 3$ .
Step 3: Identify $c$ .
The constant term is $10$ . Thus, $c = 10$ .

Comparing these coefficients to the provided choices, the correct answer is:

$a = -2, b = 3, c = 10$ .

Therefore, the correct choice is Choice 4.

Final Answer

$a=-2,b=3,c=10$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations follow $ax^2 + bx + c$ pattern
Order Matters: First coefficient is $a = -2$ , second is $b = 3$ , third is $c = 10$
Verification: Rewrite equation as $-2x^2 + 3x + 10$ matches given form ✓

Common Mistakes

Avoid these frequent errors

Ignoring negative signs in coefficients
Don't read -2x² as having coefficient a = 2! This ignores the crucial negative sign that affects parabola direction. Always include the sign as part of the coefficient: a = -2.

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 x² negative in this equation?

The coefficient a = -2 includes the negative sign! This means the parabola opens downward instead of upward. Always include signs when identifying coefficients.

What's the difference between a, b, and c coefficients?

a is the coefficient of $x^2$ (determines parabola shape), b is the coefficient of $x$ (affects vertex position), and c is the constant term (y-intercept value).

What if there's no x term in the equation?

If there's no $x$ term visible, then b = 0. For example, in $y = 3x^2 + 5$ , we have a = 3, b = 0, c = 5.

Do I always write coefficients in a, b, c order?

Yes! Always match the standard form $ax^2 + bx + c$ . Even if the equation is rearranged, identify coefficients based on which term they belong to, not their position.

Can coefficients be fractions or decimals?

Absolutely! Coefficients can be any real numbers - positive, negative, fractions, or decimals. The key is correctly identifying which number goes with which term.

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Find the Coefficients in y=-2x²+3x+10: 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 the coefficient of x² negative in this equation?

What's the difference between a, b, and c coefficients?

What if there's no x term in the equation?

Do I always write coefficients in a, b, c order?

Can coefficients be fractions or decimals?

🌟 Unlock Your Math Potential

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