Evaluate Algebraic Expressions with Given Parameters: a = -3, b = 3, c = 7

Q: What does the standard form ax² + bx + c actually represent?

This is the general form of a quadratic function. The letters a, b, and c are coefficients - specific numbers that determine the shape and position of the parabola when graphed.

Q: Why is the order of terms important in the final expression?

Mathematical convention writes quadratic expressions in descending order of powers: x² term first, then x term, then constant. This makes it easier to identify coefficients and compare expressions.

Q: What if one of the parameters equals zero?

If a = 0: Not a quadratic anymore, becomes linearIf b = 0: No middle term, like $ -3x^2 + 7 $If c = 0: No constant term, like $ -3x^2 + 3x $

Quadratic Form with Parameter Substitution

Choose the correct algebraic expression based on the parameters:

$a=-3,b=3,c=7$

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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

00:11 We'll connect each parameter to its corresponding unknown according to the formula

00:33 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

Choose the correct algebraic expression based on the parameters:

$a=-3,b=3,c=7$

Step-by-step solution

To solve this problem, we will substitute the given values into the standard quadratic form:

Step 1: Identify the formula to use. We need the standard form of a quadratic function, which is $y = ax^2 + bx + c$ .
Step 2: Substitute the given parameters into the formula:
$a = -3$ , $b = 3$ , and $c = 7$ .
Step 3: Perform the substitution:
Substituting in, we get $y = -3x^2 + 3x + 7$ .

Therefore, the correct algebraic expression is $-3x^2 + 3x + 7$ .

This corresponds to choice 2 of the multiple-choice options provided.

Final Answer

$-3x^2+3x+7$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow $ax^2 + bx + c$ pattern
Substitution: Replace a = -3, b = 3, c = 7 directly into formula
Check: Final expression $-3x^2 + 3x + 7$ matches given parameters ✓

Common Mistakes

Avoid these frequent errors

Mixing up coefficient signs during substitution
Don't write +(-3)x² as +3x² = wrong positive coefficient! This changes the entire quadratic's behavior. Always keep the original sign when substituting negative values like a = -3.

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

What does the standard form ax² + bx + c actually represent?

This is the general form of a quadratic function. The letters a, b, and c are coefficients - specific numbers that determine the shape and position of the parabola when graphed.

Why is the order of terms important in the final expression?

Mathematical convention writes quadratic expressions in descending order of powers: x² term first, then x term, then constant. This makes it easier to identify coefficients and compare expressions.

What happens if I substitute the values in the wrong places?

You'll get a completely different quadratic! For example, putting c = 7 as the x² coefficient would give $7x^2$ instead of $-3x^2$ , creating a different parabola entirely.

How can I double-check my parameter substitution?

Compare your final expression term by term: the coefficient of x² should equal a, the coefficient of x should equal b, and the constant term should equal c.

What if one of the parameters equals zero?

If a = 0: Not a quadratic anymore, becomes linear
If b = 0: No middle term, like $-3x^2 + 7$
If c = 0: No constant term, like $-3x^2 + 3x$

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Evaluate Algebraic Expressions with Given Parameters: a = -3, b = 3, c = 7

Quadratic Form with Parameter Substitution

❤️ 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

What does the standard form ax² + bx + c actually represent?

Why is the order of terms important in the final expression?

What happens if I substitute the values in the wrong places?

How can I double-check my parameter substitution?

What if one of the parameters equals zero?

🌟 Unlock Your Math Potential

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