Craft an Algebraic Expression with Given Constants: a=5, b=3, c=-4

Q: What does 'standard form' mean for quadratic expressions?

Standard form is $ ax^2 + bx + c $, where a is the coefficient of x², b is the coefficient of x, and c is the constant term. This order never changes!

Q: Why is the answer positive 5x² and not negative 5x²?

Because we're given a = 5, which is positive. The coefficient a goes directly in front of x². If a were -5, then we'd have $ -5x^2 $.

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

While mathematically equivalent, standard form requires the specific order: x² term first, x term second, constant term last. This makes it easier to identify coefficients.

Quadratic Expressions with Standard Form

Create an algebraic expression based on the following parameters:

$a=5,b=3,c=-4$

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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

00:10 Connect the parameter to its corresponding variable according to the formula

00:26 Write the function in its reduced form

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

Create an algebraic expression based on the following parameters:

$a=5,b=3,c=-4$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the general form of the quadratic expression.
Step 2: Substitute the given values $a = 5$ , $b = 3$ , and $c = -4$ into the quadratic form.
Step 3: Write down the resultant expression.

Now, let's work through each step:
Step 1: The general form of a quadratic expression is $ax^2 + bx + c$ .
Step 2: We are given $a = 5$ , $b = 3$ , and $c = -4$ . Substituting these into the expression, we get:

$5x^2 + 3x - 4$

Therefore, the solution to the problem is $5x^2 + 3x - 4$ .

Final Answer

$5x^2+3x-4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic expressions follow the pattern $ax^2 + bx + c$
Substitution: Replace a=5, b=3, c=-4 to get $5x^2 + 3x - 4$
Verification: Check coefficients match given values: a=5, b=3, c=-4 ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient positions in standard form
Don't put coefficients in wrong positions like $5x^2 - 4x + 3$ = mixing up b and c values! This creates a completely different expression. Always follow the exact order: $ax^2 + bx + c$ where the first coefficient goes with x², second with x, third is the constant.

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 'standard form' mean for quadratic expressions?

Standard form is $ax^2 + bx + c$ , where a is the coefficient of x², b is the coefficient of x, and c is the constant term. This order never changes!

Why is the answer positive 5x² and not negative 5x²?

Because we're given a = 5, which is positive. The coefficient a goes directly in front of x². If a were -5, then we'd have $-5x^2$ .

What happens to the negative sign in c = -4?

The negative sign stays with the constant! Since c = -4, we write $+(-4)$ , which simplifies to $-4$ in the final expression.

Can I rearrange the terms in a different order?

While mathematically equivalent, standard form requires the specific order: x² term first, x term second, constant term last. This makes it easier to identify coefficients.

What if one of the coefficients was zero?

If a coefficient is zero, that term disappears! For example, if b = 0, you'd get $5x^2 + 0x - 4 = 5x^2 - 4$ . The x term vanishes completely.

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Craft an Algebraic Expression with Given Constants: a=5, b=3, c=-4

Quadratic Expressions with Standard Form

❤️ 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 'standard form' mean for quadratic expressions?

Why is the answer positive 5x² and not negative 5x²?

What happens to the negative sign in c = -4?

Can I rearrange the terms in a different order?

What if one of the coefficients was zero?

🌟 Unlock Your Math Potential

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