Parameter Challenge: Find the Representation for a=-3, b=4, c=-15

Q: Why is it +4x and not -4x when b=4?

When b=4, you substitute +4 directly into the standard form $ ax^2 + bx + c $. The + sign is already there, so b=4 gives you +4x, not -4x!

Q: How do I remember which coefficient goes where?

Use the pattern a-b-c: a goes with x², b goes with x¹, and c stands alone (no variable). Just match them up in order!

Q: Can I write the terms in a different order?

For standard form, always write terms in descending order of powers: x² term first, then x term, then constant. This makes it easier to identify coefficients correctly.

Quadratic Forms with Given Coefficients

Find the appropriate representation based on the parameters

$a=-3,b=4,c=-15$

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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 We'll use the formula to represent a quadratic equation

00:11 Connect the parameter to the corresponding variable according to the formula

00:29 Write the function in its reduced form

00:36 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

Find the appropriate representation based on the parameters

$a=-3,b=4,c=-15$

Step-by-step solution

To solve this problem, we need to construct the quadratic equation using the given parameters:

Step 1: Identify the parameters from the problem statement:
- $a = -3$ , $b = 4$ , $c = -15$ .
Step 2: Apply these parameters to the standard form of a quadratic equation:
- The standard form is $y = ax^2 + bx + c$ .
Step 3: Substitute the given values into the standard form:
- Substitute $a = -3$ , $b = 4$ , $c = -15$ into $y = ax^2 + bx + c$ .

By substitution, the equation becomes:

$y = -3x^2 + 4x - 15$ .

This expression correctly represents the quadratic equation using the specified parameters.

Therefore, the correct answer is option 3: $-3x^2 + 4x - 15$ .

Final Answer

$-3x^2+4x-15$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equation follows ax² + bx + c pattern
Substitution: Replace a=-3, b=4, c=-15 into -3x² + 4x + (-15)
Check: Verify each coefficient matches: -3 for x², +4 for x, -15 constant ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient signs during substitution
Don't write -3x² - 4x - 15 when b=4 and c=-15 = wrong signs everywhere! Students often flip signs incorrectly when substituting negative values. Always substitute exactly as given: b=4 means +4x, c=-15 means -15.

Practice Quiz

Test your knowledge with interactive questions

Identify the coefficients based on the following equation

$$ y=x^2 $$

FAQ

Everything you need to know about this question

Why is it +4x and not -4x when b=4?

When b=4, you substitute +4 directly into the standard form $ax^2 + bx + c$ . The + sign is already there, so b=4 gives you +4x, not -4x!

What's the difference between c=-15 and writing -15?

They're the same! When c=-15, you substitute -15 into the standard form. So $ax^2 + bx + c$ becomes $ax^2 + bx + (-15)$ , which simplifies to $ax^2 + bx - 15$ .

How do I remember which coefficient goes where?

Use the pattern a-b-c: a goes with x², b goes with x¹, and c stands alone (no variable). Just match them up in order!

What if one of the coefficients is positive and another is negative?

That's totally normal! Each coefficient keeps its own sign. So a=-3 makes -3x², b=4 makes +4x, and c=-15 makes -15. Don't change the signs - just substitute directly.

Can I write the terms in a different order?

For standard form, always write terms in descending order of powers: x² term first, then x term, then constant. This makes it easier to identify coefficients correctly.

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Parameter Challenge: Find the Representation for a=-3, b=4, c=-15

Quadratic Forms 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

Why is it +4x and not -4x when b=4?

What's the difference between c=-15 and writing -15?

How do I remember which coefficient goes where?

What if one of the coefficients is positive and another is negative?

Can I write the terms in a different order?

🌟 Unlock Your Math Potential

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