# HSA-REI.B.4

Solve quadratic equations in one variable.

**a**
Use the method of completing the square to transform any quadratic equation in $x$ into an equation of the form $(x - p)^2 = q$ that has the same solutions. Derive the quadratic formula from this form.

**b**
Solve quadratic equations by inspection (e.g., for $x^2 = 49$), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as $a \pm bi$ for real numbers $a$ and $b$.

## Tasks

Springboard Dive

Building a General Quadratic Function

Braking Distance

Two Squares are Equal

Completing the square

Visualizing Completing the Square

Vertex of a parabola with complex roots

Quadratic Sequence 1

Quadratic Sequence 2

Quadratic Sequence 3

Zero Product Property 4