Create an Algebraic Expression with Variables a=4, b=-2, c=16

Q: Why is the middle term -2x instead of +2x when b=-2?

When b = -2, you substitute this entire value including the negative sign. So bx becomes (-2)x = -2x. The negative is part of the coefficient, not a separate operation!

Q: What if I get confused about which coefficient goes where?

Remember the pattern: $ ax^2 + bx + c $. The first coefficient (a) goes with x², the second (b) goes with x, and the third (c) stands alone.

Q: Can the coefficients be any numbers?

Yes! Coefficients can be positive, negative, fractions, or decimals. Just make sure to substitute them exactly as given, including any negative signs.

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

Check that your expression has the right degree (highest power is 2) and that each coefficient matches what was given: a with x², b with x, and c as the constant term.

Q: What's the difference between this and solving a quadratic equation?

Here you're just creating the expression using given coefficients. Solving would mean finding x-values that make the expression equal zero - that's a different process!

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following parameters:

$a=4,b=-2,c=16$

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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 Use the formula to represent a quadratic equation

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

00:29 Write the function in its reduced form

00:38 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:

$a=4,b=-2,c=16$

Step-by-step solution

To solve this problem, we need to form a quadratic expression using the given parameters.

Step 1: Identify the given coefficients as follows: $a = 4$ , $b = -2$ , $c = 16$ .
Step 2: Use the standard quadratic form $ax^2 + bx + c$ .
Step 3: Substitute the given values into the quadratic form to get the expression $4x^2 - 2x + 16$ .

Now, let's perform the substitution:

Substituting the values:
$a = 4$ : This gives us $4x^2$ .
$b = -2$ : This gives us $-2x$ .
$c = 16$ : This remains as $+16$ .

Thus, the complete quadratic expression is $4x^2 - 2x + 16$ .

Therefore, the solution to the problem is $\boxed{4x^2 - 2x + 16}$ .

Final Answer

$4x^2-2x+16$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow the pattern ax² + bx + c
Substitution: Replace a=4, b=-2, c=16 to get 4x² - 2x + 16
Check: Verify each coefficient matches: a=4 for x², b=-2 for x, c=16 constant ✓

Common Mistakes

Avoid these frequent errors

Ignoring negative signs when substituting coefficients
Don't write b=-2 as +2x instead of -2x = wrong expression! The negative sign is part of the coefficient value and must be preserved. Always keep the sign with the coefficient when substituting into ax² + 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

Why is the middle term -2x instead of +2x when b=-2?

When b = -2, you substitute this entire value including the negative sign. So bx becomes (-2)x = -2x. The negative is part of the coefficient, not a separate operation!

What if I get confused about which coefficient goes where?

Remember the pattern: $ax^2 + bx + c$ . The first coefficient (a) goes with x², the second (b) goes with x, and the third (c) stands alone.

Can the coefficients be any numbers?

Yes! Coefficients can be positive, negative, fractions, or decimals. Just make sure to substitute them exactly as given, including any negative signs.

How do I know if my expression is correct?

Check that your expression has the right degree (highest power is 2) and that each coefficient matches what was given: a with x², b with x, and c as the constant term.

What's the difference between this and solving a quadratic equation?

Here you're just creating the expression using given coefficients. Solving would mean finding x-values that make the expression equal zero - that's a different process!

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Create an Algebraic Expression with Variables a=4, b=-2, c=16

Quadratic Expressions 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 the middle term -2x instead of +2x when b=-2?

What if I get confused about which coefficient goes where?

Can the coefficients be any numbers?

How do I know if my expression is correct?

What's the difference between this and solving a quadratic equation?

🌟 Unlock Your Math Potential

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