Develop an Algebraic Expression Using a=3, b=4, c=-15

Q: What does each letter represent in the standard 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 variable attached).

Q: Why is the answer 3x² + 4x - 15 and not just the numbers?

The question asks for an algebraic expression, which means we need variables (like x). We're creating the expression by substituting the given values into the standard quadratic form.

Q: How do I remember the correct order of terms?

Remember "Alphabet order": a goes with the highest power ($ x^2 $), b with the middle power (x), and c is the constant (no x).

Q: What's the difference between a function and an expression?

An expression like $ 3x^2 + 4x - 15 $ is just the mathematical phrase. A function would be $ f(x) = 3x^2 + 4x - 15 $ or $ y = 3x^2 + 4x - 15 $.

Quadratic Expressions with Given Coefficients

Create an algebraic expression based on the following 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 the parameters to a quadratic function

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

00:16 Connect the parameter to its corresponding unknown according to the formula

00:36 Write the function in its reduced form

00:46 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:

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

Step-by-step solution

To create an algebraic expression based on the parameters provided, we need to follow these steps:

Step 1: Recognize the standard form of a quadratic function: $y = ax^2 + bx + c$ .
Step 2: Identify and substitute the given values $a = 3$ , $b = 4$ , and $c = -15$ into this form.
Step 3: Substitute to form the expression: $y = 3x^2 + 4x - 15$ .

Step 1: We recognize that we are dealing with a quadratic equation in the form $y = ax^2 + bx + c$ .

Step 2: Using the values given in the problem statement, substitute $a = 3$ , $b = 4$ , and $c = -15$ into this standard form equation:

$y = ax^2 + bx + c \rightarrow y = 3x^2 + 4x - 15$

Step 3: This substitution gives us the algebraic expression:

$3x^2 + 4x - 15$

Therefore, the expression based on the given parameters is $\mathbf{3x^2 + 4x - 15}$ .

Final Answer

$3x^2+4x-15$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow $ax^2 + bx + c$ pattern
Direct Substitution: Replace a=3, b=4, c=-15 into $ax^2 + bx + c$
Verification: Check coefficient order matches a, b, c values exactly ✓

Common Mistakes

Avoid these frequent errors

Mixing up coefficient positions
Don't put a=3 in the wrong position like $x^2 + 3x - 15$ = incorrect expression! This mixes up the a and b coefficients, creating a completely different quadratic. Always place a with $x^2$ , b with x, and c as the constant term.

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 standard 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 variable attached).

Why is the answer 3x² + 4x - 15 and not just the numbers?

The question asks for an algebraic expression, which means we need variables (like x). We're creating the expression by substituting the given values into the standard quadratic form.

What if one of the coefficients was zero?

If a coefficient is zero, that term disappears! For example, if a=0, you'd get bx + c (a linear expression). If b=0, you'd get ax² + c.

Do I need to simplify or factor this expression?

Not unless specifically asked! The question only requires creating the expression $3x^2 + 4x - 15$ . Factoring would be a separate step if needed.

How do I remember the correct order of terms?

Remember "Alphabet order": a goes with the highest power ( $x^2$ ), b with the middle power (x), and c is the constant (no x).

What's the difference between a function and an expression?

An expression like $3x^2 + 4x - 15$ is just the mathematical phrase. A function would be $f(x) = 3x^2 + 4x - 15$ or $y = 3x^2 + 4x - 15$ .

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Develop an Algebraic Expression Using a=3, b=4, c=-15

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

What does each letter represent in the standard form?

Why is the answer 3x² + 4x - 15 and not just the numbers?

What if one of the coefficients was zero?

Do I need to simplify or factor this expression?

How do I remember the correct order of terms?

What's the difference between a function and an expression?

🌟 Unlock Your Math Potential

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