Find the Constant Term c in y = -x² + 25x: Coefficient Analysis

Q: Why is the constant term 0 if there's no number at the end?

When a term is missing from a polynomial, its coefficient is automatically 0. Think of it like this: $ y = -x^2 + 25x $ is really $ y = -x^2 + 25x + 0 $ - we just don't write the +0 part!

Q: How can I remember which coefficient is which?

Use the powers of x as your guide! In $ ax^2 + bx + c $: a goes with $ x^2 $, b goes with $ x^1 $, and c goes with $ x^0 = 1 $ (the constant).

Q: What if the equation is written differently, like x² + 25x - x²?

Always combine like terms first! Group all $ x^2 $ terms, all $ x $ terms, and all constants separately. Then identify a, b, and c from the simplified form.

Q: Does the order of terms matter when finding coefficients?

No! Whether you see $ 25x - x^2 $ or $ -x^2 + 25x $, the coefficients are the same. Just match each coefficient with its corresponding power of x.

Q: What happens if there's no x² term?

If the $ x^2 $ term is missing, then a = 0 and you have a linear function, not a quadratic! The same rule applies - missing terms have coefficient 0.

Quadratic Coefficients with Missing Constant Terms

a = coefficient of x²

b = coefficient of x

c = coefficient of the constant term

What is the value of $c$ in the function $y=-x^2+25x$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the coefficient, C.

00:11 We will use the quadratic equation formula.

00:16 Notice that the coefficient, C, is the constant term.

00:20 Now, let's compare our formula to the given equation and identify the coefficients.

00:40 If there is no constant term, it means it's zero.

00:50 And that's how we solve this question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

a = coefficient of x²

b = coefficient of x

c = coefficient of the constant term

What is the value of $c$ in the function $y=-x^2+25x$ ?

Step-by-step solution

Let's recall the general form of the quadratic function:

$y=ax^2+bx+c$ The function given in the problem is:

$y=-x^2+25x$ $c$ is the free term (meaning the coefficient of the term with power 0),

In the function in the problem there is no free term,

Therefore, we can identify that:

$c=0$ Therefore, the correct answer is answer A.

Final Answer

$c=0$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic functions follow $y = ax^2 + bx + c$ format
Identification: In $y = -x^2 + 25x$ , a = -1, b = 25, c = 0
Verification: Rewrite as $y = -x^2 + 25x + 0$ to confirm c = 0 ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficients with constant terms
Don't think c = 25 just because 25 appears in the equation! The coefficient 25 belongs to the x term, not the constant term. Always identify which variable each number multiplies - c is the term with no variable attached.

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=3x-10+5x^2 $$

FAQ

Everything you need to know about this question

Why is the constant term 0 if there's no number at the end?

When a term is missing from a polynomial, its coefficient is automatically 0. Think of it like this: $y = -x^2 + 25x$ is really $y = -x^2 + 25x + 0$ - we just don't write the +0 part!

How can I remember which coefficient is which?

Use the powers of x as your guide! In $ax^2 + bx + c$ : a goes with $x^2$ , b goes with $x^1$ , and c goes with $x^0 = 1$ (the constant).

What if the equation is written differently, like x² + 25x - x²?

Always combine like terms first! Group all $x^2$ terms, all $x$ terms, and all constants separately. Then identify a, b, and c from the simplified form.

Does the order of terms matter when finding coefficients?

No! Whether you see $25x - x^2$ or $-x^2 + 25x$ , the coefficients are the same. Just match each coefficient with its corresponding power of x.

What happens if there's no x² term?

If the $x^2$ term is missing, then a = 0 and you have a linear function, not a quadratic! The same rule applies - missing terms have coefficient 0.

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