Constructing an Algebraic Expression: Parameters a = -1, b = 0, c = 0 Explained

Q: Why do the b and c terms disappear when they equal zero?

When b = 0 and c = 0, those terms become $ 0 \cdot x = 0 $ and just $ 0 $. Adding zero doesn't change the expression, so we can omit them entirely!

Q: What does the negative coefficient tell me about the parabola?

The negative coefficient $ a = -1 $ means the parabola opens downward (like an upside-down U). If it were positive, it would open upward.

Q: Is -x² the same as (-x)²?

No! $ -x^2 $ means the negative of x squared, while $ (-x)^2 $ means negative x, then squared. For example: $ -3^2 = -9 $ but $ (-3)^2 = 9 $.

Q: How do I check if my expression is correct?

Test with a simple value like x = 2: $ -x^2 = -(2)^2 = -4 $. Then verify this matches the original form: $ (-1)(2)^2 + 0(2) + 0 = -4 $ ✓

Q: What if I had different parameter values?

Always substitute exactly what's given! If $ a = 2, b = -3, c = 1 $, you'd get $ 2x^2 - 3x + 1 $. The process stays the same: substitute and simplify.

Quadratic Functions with Zero Linear Terms

Create an algebraic expression based on the following parameters:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert the parameters to a quadratic function

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

00:12 We'll connect each parameter to its corresponding variable according to the formula

00:29 We'll write the function in its reduced form

00:48 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

Create an algebraic expression based on the following parameters:

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

Step-by-step solution

We begin by noting that the general form of a quadratic function is represented by the equation:

$y = ax^2 + bx + c$

Given the parameters $a = -1$ , $b = 0$ , and $c = 0$ , we substitute these values into the equation:

$y = (-1)x^2 + (0)x + 0$

Simplifying the expression, we get:

$y = -x^2$

Thus, the algebraic expression representing the given parameters is $-x^2$ .

The correct answer choice that corresponds to this expression is:

$-x^2$

Final Answer

$-x^2$

Key Points to Remember

Essential concepts to master this topic

General Form: Use standard quadratic template $y = ax^2 + bx + c$
Substitution: Replace parameters: $y = (-1)x^2 + (0)x + 0$
Simplify: Remove zero terms to get $y = -x^2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the negative coefficient
Don't write x² when a = -1, ignoring the negative sign = wrong expression! The coefficient directly multiplies the x² term and must be preserved. Always include the coefficient exactly as given, so a = -1 becomes -x².

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 do the b and c terms disappear when they equal zero?

When b = 0 and c = 0, those terms become $0 \cdot x = 0$ and just $0$ . Adding zero doesn't change the expression, so we can omit them entirely!

What does the negative coefficient tell me about the parabola?

The negative coefficient $a = -1$ means the parabola opens downward (like an upside-down U). If it were positive, it would open upward.

Is -x² the same as (-x)²?

No! $-x^2$ means the negative of x squared, while $(-x)^2$ means negative x, then squared. For example: $-3^2 = -9$ but $(-3)^2 = 9$ .

How do I check if my expression is correct?

Test with a simple value like x = 2: $-x^2 = -(2)^2 = -4$ . Then verify this matches the original form: $(-1)(2)^2 + 0(2) + 0 = -4$ ✓

What if I had different parameter values?

Always substitute exactly what's given! If $a = 2, b = -3, c = 1$ , you'd get $2x^2 - 3x + 1$ . The process stays the same: substitute and simplify.

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Constructing an Algebraic Expression: Parameters a = -1, b = 0, c = 0 Explained

Quadratic Functions with Zero Linear Terms

❤️ 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 do the b and c terms disappear when they equal zero?

What does the negative coefficient tell me about the parabola?

Is -x² the same as (-x)²?

How do I check if my expression is correct?

What if I had different parameter values?

🌟 Unlock Your Math Potential

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