Quadratics
Square the variable and the straight line bends. What changes, and how do you still solve it?
Where you are 12 inside
What this area is about
A quadratic is an expression like ax^2 + bx + c, with the variable squared and no higher. Its graph is a parabola, a curve that turns once. Squaring makes it hard to solve: x appears twice, and an equation can have two real answers, one, or none.
How these fit together
The object. Quadratic expressions and parabolas sets up the object, its graph and its vertex. Roots, zeros and x-intercepts shows that solutions, zeros and crossing points coincide.
Ways to solve ax^2 + bx + c = 0. Solving quadratics with square roots handles a variable only inside a square, as in x^2 = 25. Solving quadratics by factoring is fastest when the expression factors. Completing the square always works: Completing the square for a plain x^2, then Completing the square, leading coefficient not one. The quadratic formula is that method done once, in general, and its discriminant, b^2 - 4ac, counts the real solutions in advance.
Forms of the graph. Vertex form: reading, converting and graphing puts the turning point in the equation and covers moving and stretching the curve. Factored form puts the roots there instead.
Using it. Quadratic inequalities, Maximum, minimum and projectile problems and Fitting a quadratic to data.
A path through it
Expressions and parabolas; square roots, factoring, roots and intercepts; completing the square, both cases, and the formula; vertex form, factored form, inequalities, best values; fitting last.
After this: quadratic functions, systems where a line meets a curve, and complex numbers, where every quadratic equation has a solution.