Find the Constant Term c in y = 3x² + 5: Quadratic Equation Analysis

Q: Why do I need to rearrange the equation first?

Rearranging to standard form makes it crystal clear which number goes with which part! When you see $ y = 5 + 3x^2 $, it's easy to mix up the coefficients.

Q: What if there's no x term like in this equation?

That's totally normal! When there's no x term, it means b = 0. You can think of it as $ 3x^2 + 0 \cdot x + 5 $ - the $ 0 \cdot x $ part is just invisible.

Q: How do I remember which coefficient is which?

Use this memory trick: a goes with the squared term, b goes with the basic x term, and c is the constant (no variable at all).

Standard Form with Constant Term Identification

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $c$ in this quadratic equation:

$y=5+3x^2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find coefficient C

00:03 We'll use the quadratic equation formula

00:08 We can see that coefficient C is of the independent number

00:20 If we don't have the X term, it's multiplied by 0

00:27 We'll compare the formula to our equation and find the coefficients

00:42 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

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

what is the value of $c$ in this quadratic equation:

$y=5+3x^2$

Step-by-step solution

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

Step 1: Compare the given equation $y = 5 + 3x^2$ to the standard form $ax^2 + bx + c$ .
Step 2: Identify the terms corresponding to $a$ , $b$ , and $c$ .

Now, let's work through each step:
Step 1: The given equation is $y = 5 + 3x^2$ . Rearranging it in the standard form, we have $y = 3x^2 + 0\cdot x + 5$ .

Step 2: From this arrangement, it's clear that:
- $a = 3$ (the coefficient of $x^2$ )
- $b = 0$ (there is no $x$ term, so its coefficient is 0)
- $c = 5$ (the constant term)

Therefore, the value of $c$ is $\ c=5$ .

Final Answer

$c=5$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations follow the pattern $ax^2 + bx + c$
Rearrangement: Rewrite $y = 5 + 3x^2$ as $y = 3x^2 + 0x + 5$
Verification: Check that constant term has no variable: c = 5 ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient positions in rearranged equations
Don't assume c = 3 just because 3 appears first in y = 5 + 3x² = wrong identification! The position of terms doesn't determine their role - only their mathematical function does. Always rearrange to standard form ax² + bx + c first, then identify each coefficient by its variable.

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=3x-10+5x^2 $$

FAQ

Everything you need to know about this question

Why do I need to rearrange the equation first?

Rearranging to standard form makes it crystal clear which number goes with which part! When you see $y = 5 + 3x^2$ , it's easy to mix up the coefficients.

What if there's no x term like in this equation?

That's totally normal! When there's no x term, it means b = 0. You can think of it as $3x^2 + 0 \cdot x + 5$ - the $0 \cdot x$ part is just invisible.

How do I remember which coefficient is which?

Use this memory trick: a goes with the squared term, b goes with the basic x term, and c is the constant (no variable at all).

Can the constant term be negative?

Absolutely! The constant term c can be positive, negative, or even zero. It's just whatever number stands alone without any variable attached to it.

What happens if I identify the wrong coefficient?

You'll get the wrong answer and won't understand the equation's behavior! Each coefficient has a specific job - a controls the parabola's width, b affects the vertex position, and c is the y-intercept.

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