### IA.REI: Reasoning with Equations and Inequalities

#### IA.AREI.4: Solve mathematical and real-world problems involving quadratic equations in one variable.

IA.AREI.4.a: Use the method of completing the square to transform any quadratic equation in 𝑥 into an equation of the form (x − h)² = k that has the same solutions. Derive the quadratic formula from this form.

IA.AREI.4.b: Solve quadratic equations by inspection, 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 + bi for real numbers a and b.

### IA.ASE: Structure and Expressions

#### IA.ASE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

IA.ASE.3.a: Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation.

IA.ASE.3.b: Determine the maximum or minimum value of a quadratic function by completing the square.

### IA.FBF: Building Functions

#### IA.FBF.1: Write a function that describes a relationship between two quantities.

IA.FBF.1.a: Write a function that models a relationship between two quantities using both explicit expressions and a recursive process and by combining standard forms using addition, subtraction, multiplication and division to build new functions.

IA.FBF.1.b: Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations.

### IA.FIF: Interpreting Functions

#### IA.FIF.8: Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function.

IA.FIF.8.b: Interpret expressions for exponential functions by using the properties of exponents.

### IA.NCNS: Complex Number System

#### IA.NCNS.7: Solve quadratic equations in one variable that have complex solutions.

Correlation last revised: 9/16/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.