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Advanced Mathematics 2200
Relations and Functions
6. NL.SO.2200RF3
6.3 Quadratic function in general form: y = ax^2 + bx + c
Quadratic Function in General Form: y = ax^2 + bx + c
Understand the general (standard) form of a quadratic function, what each coefficient controls, and how to pull the vertex and intercepts straight out of it.
What You'll Learn
The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are real numbers and a is not zero.
The sign of a tells you whether the parabola opens upward or downward, and larger absolute values of a make it narrower.
The constant c is always the y-intercept of the graph, since setting x = 0 gives y = c.
The vertex of the parabola can be found directly from general form using x = negative b divided by 2a, then substituting back to get the y-coordinate.
Converting general form to vertex form by completing the square makes the vertex and transformations even easier to read off.
What You'll Practice
1
Finding y-intercepts from quadratic equations in general form
2
Solving for x-intercepts by factoring trinomials
3
Calculating vertex coordinates using x-intercepts and substitution
4
Graphing complete parabolas from intercepts and vertices
Why This Matters
Mastering quadratic functions in general form prepares you for advanced algebra, physics, and calculus. Graphing parabolas is essential for modeling real-world scenarios like projectile motion, profit maximization, and engineering design problems you'll encounter throughout STEM courses.
This Unit Includes
1 Video lesson
Learning resources
Skills
Quadratic Functions
Parabolas
Intercepts
Vertex
Factoring
Graphing
General Form
NL Curriculum Aligned