Solve y=2x²-5x+6: Complete Quadratic Function Guide

Quadratic Functions with Standard Form Identification

y=2x25x+6 y=2x^2-5x+6

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the function coefficients
00:03 Use the formula to represent a quadratic equation
00:18 Separate the variable from the coefficient
00:31 Compare the formula to our equation and find the coefficients
00:40 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=2x25x+6 y=2x^2-5x+6

2

Step-by-step solution

In fact, a quadratic equation is composed as follows:

y = ax²-bx-c

 

That is,

a is the coefficient of x², in this case 2.
b is the coefficient of x, in this case 5.
And c is the number without a variable at the end, in this case 6.

3

Final Answer

a=2,b=5,c=6 a=2,b=-5,c=6

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: y=ax2+bx+c y = ax^2 + bx + c identifies quadratic coefficients
  • Technique: For y=2x25x+6 y = 2x^2 - 5x + 6 , identify a=2, b=-5, c=6
  • Check: Verify coefficients match positions: x² term, x term, constant ✓

Common Mistakes

Avoid these frequent errors
  • Missing the negative sign in coefficient b
    Don't ignore the negative sign in -5x when identifying b = coefficient of x! This gives wrong coefficient values for quadratic formulas. Always include the sign as part of the coefficient: b = -5, not b = 5.

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 b = -5 instead of b = 5?

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In y=2x25x+6 y = 2x^2 - 5x + 6 , the coefficient of x includes its sign. Since we have -5x, the coefficient b = -5. The negative sign is part of the coefficient, not separate!

What if the equation isn't written in standard form?

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Always rearrange first! Move all terms to one side so you have ax2+bx+c=0 ax^2 + bx + c = 0 or y=ax2+bx+c y = ax^2 + bx + c . Then identify your coefficients.

Can any of the coefficients a, b, or c be zero?

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Yes! b and c can be zero, but a cannot be zero in a quadratic function. If a = 0, it becomes a linear function instead.

How do I remember which coefficient is which?

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Use the pattern: a goes with x², b goes with x¹, c goes with x⁰ (the constant). They're in alphabetical order matching decreasing powers!

What if there's no x term or constant term?

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If a term is missing, its coefficient is zero. For example, y=3x2+7 y = 3x^2 + 7 means a = 3, b = 0, c = 7 because there's no x term.

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