Analyze the Quadratic Expression: y = x² + 10x Step by Step

Quadratic Functions with Missing Constant Term

y=x2+10x y=x^2+10x

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the function's coefficients
00:03 We'll use the formula to represent a quadratic equation
00:10 We'll arrange the equation to match the formula
00:25 We'll separate the unknown from the coefficient
00:35 We'll compare the formula to our equation and find the coefficients
00:48 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

y=x2+10x y=x^2+10x

2

Step-by-step solution

Here we have a quadratic equation.

A quadratic equation is always constructed like this:

 

y=ax2+bx+c y = ax²+bx+c

 

Where a, b, and c are generally already known to us, and the X and Y points need to be discovered.

Firstly, it seems that in this formula we do not have the C,

Therefore, we understand it is equal to 0.

c=0 c = 0

 

a is the coefficient of X², here it does not have a coefficient, therefore

a=1 a = 1

 

b=10 b= 10

is the number that comes before the X that is not squared.

 

3

Final Answer

a=1,b=10,c=0 a=1,b=10,c=0

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: Every quadratic follows y=ax2+bx+c y = ax^2 + bx + c
  • Missing Terms: When c isn't shown, it equals 0 like in x2+10x x^2 + 10x
  • Coefficients: Find a=1, b=10, c=0 by comparing to standard form ✓

Common Mistakes

Avoid these frequent errors
  • Confusing coefficient positions
    Don't assign b=1 and a=10 = completely wrong coefficients! This happens when students mix up which number goes with which variable. Always match coefficients by looking at the exponents: a goes with x², b goes with x¹, c is the constant.

Practice Quiz

Test your knowledge with interactive questions

What is the value of the coefficient \( c \) in the equation below?

\( 4x^2+9x-2 \)

FAQ

Everything you need to know about this question

Why is the coefficient of x² equal to 1 when I don't see a number there?

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When no number appears before a variable, the coefficient is always 1. Think of x2 x^2 as 1x2 1x^2 - the 1 is just invisible!

How do I know c = 0 if it's not written in the equation?

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If there's no constant term (number without x), then c = 0. It's like saying you have 0 extra units. The equation x2+10x x^2 + 10x is really x2+10x+0 x^2 + 10x + 0 .

What's the difference between a, b, and c in a quadratic?

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a is the coefficient of x2 x^2 (controls the parabola's width), b is the coefficient of x x (affects the vertex position), and c is the constant term (the y-intercept).

Can I have a quadratic with just x² and no other terms?

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Yes! For example, y=3x2 y = 3x^2 has a=3, b=0, c=0. Missing terms just mean their coefficients are zero, but it's still a complete quadratic function.

How do I remember which coefficient is which?

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Use alphabetical order! In ax2+bx+c ax^2 + bx + c , the letters a, b, c match the decreasing powers of x: x², x¹, x⁰ (which is just the constant).

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