Construct an Algebraic Expression with Constants: a = -2, c = 3, 4

Q: What does each letter represent in the quadratic form?

In $ ax^2 + bx + c $: a is the coefficient of $ x^2 $, b is the coefficient of $ x $, and c is the constant term (no x).

Q: Why is the first answer choice wrong if it has the right numbers?

The answer $ 2x^2 + 3x + 4 $ uses positive 2 instead of negative 2. When a = -2, you must include the negative sign: $ -2x^2 $.

Q: Do I need to simplify the expression further?

No simplification needed! The expression $ -2x^2 + 3x + 4 $ is already in standard form with terms arranged by decreasing powers of x.

Q: How do I remember which coefficient goes where?

Think alphabetically: a goes with $ x^2 $, b goes with $ x $, and c stands alone as the constant. The powers decrease from left to right!

Quadratic Expression Construction with Given Coefficients

Create an algebraic expression based on the following parameters:

$a=-2,c=3,c=4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert from parameters to quadratic function

00:03 Match between the parameter and the corresponding term

00:06 Write according to the quadratic function formula

00:09 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:

$a=-2,c=3,c=4$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the given parameters from the problem statement. We have $a = -2$ , $b = 3$ , and $c = 4$ .
Step 2: Substitute these values into the standard quadratic formula $y = ax^2 + bx + c$ .
Step 3: Write the algebraic expression using the substituted values.

Now let's execute these steps:

Step 1: We know $a = -2$ , $b = 3$ , and $c = 4$ .

Step 2: Substitute the values into the quadratic function:

$y = (-2)x^2 + (3)x + 4$

Step 3: Simplify to present the function:

The algebraic expression is $y = -2x^2 + 3x + 4$ .

Therefore, the solution to the problem is $-2x^2 + 3x + 4$ .

Final Answer

$-2x^2+3x+4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow $ax^2 + bx + c$ format
Substitution: Replace a=-2, b=3, c=4 to get $-2x^2 + 3x + 4$
Verification: Check coefficient signs match given values: negative a, positive b and c ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient signs or positions
Don't write $2x^2 + 3x + 4$ when a = -2! This ignores the negative sign and gives wrong expression. Always preserve the exact sign of each coefficient when substituting into $ax^2 + bx + c$ .

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 each letter represent in the quadratic form?

In $ax^2 + bx + c$ : a is the coefficient of $x^2$ , b is the coefficient of $x$ , and c is the constant term (no x).

Why is the first answer choice wrong if it has the right numbers?

The answer $2x^2 + 3x + 4$ uses positive 2 instead of negative 2. When a = -2, you must include the negative sign: $-2x^2$ .

What if I see 'c' used twice in the problem statement?

This appears to be a typo in the problem. Based on the explanation, we have a = -2, b = 3, and c = 4 for the standard quadratic form.

Do I need to simplify the expression further?

No simplification needed! The expression $-2x^2 + 3x + 4$ is already in standard form with terms arranged by decreasing powers of x.

How do I remember which coefficient goes where?

Think alphabetically: a goes with $x^2$ , b goes with $x$ , and c stands alone as the constant. The powers decrease from left to right!

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Construct an Algebraic Expression with Constants: a = -2, c = 3, 4

Quadratic Expression Construction with Given Coefficients

❤️ 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 each letter represent in the quadratic form?

Why is the first answer choice wrong if it has the right numbers?

What if I see 'c' used twice in the problem statement?

Do I need to simplify the expression further?

How do I remember which coefficient goes where?

🌟 Unlock Your Math Potential

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