# A.4c and *A.4b - Quadratic Equations

A.4    The student will solve multistep linear and quadratic equations in two variables, including

c)  solving quadratic equations algebraically and graphically;

Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions.

A.4  The student will solve

b)  quadratic equations in one variable algebraically;

Bloom's Level:  Apply

### BIG IDEAS

• I can find the best trajectory for swooshing a basketball from center court to make 3 points and I can determine the curved course for a rocket launched to Mars.
• I will be able to write symbolic representations of the way numbers behave and will know that in order to maintain equality, an operation performed on one side must also be performed on the other side.

### UNDERSTANDING THE STANDARD

• Real-world problems can be interpreted, represented, and solved using linear and quadratic equations.
• The process of solving linear and quadratic equations can be modeled in a variety of ways, using concrete, pictorial, and symbolic representations.
• Properties of real numbers and properties of equality can be used to justify equation solutions and expression simplification.
• The zeros or the x-intercepts of the quadratic function are the real root(s) or solution(s) of the quadratic equation that is formed by setting the given quadratic expression equal to zero.

·  Each point on the graph of a linear or quadratic equation in two variables is a solution of the equation.

·  Practical problems may be interpreted, represented, and solved using linear and quadratic equations.

·  The process of solving linear and quadratic equations can be modeled in a variety of ways, using concrete, pictorial, and symbolic representations.

·  Quadratic equations in one variable may be solved algebraically by factoring and applying properties of equality or by using the quadratic formula over the set of real numbers (Algebra I) or the set of complex numbers (Algebra II).

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  A.4bSolve quadratic equations in one variable algebraically.  Solutions may be rational or irrational.

·  A.4bApply the properties of real numbers and properties of equality to simplify expressions and solve equations.

A.4c2  Identify the roots or zeros of a quadratic function over the real number system as the solutions to the quadratic equation that is formed by setting the given quadratic expression equal to zero.

·  A.7bcdIdentify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.

·  A.7cdUse the x-intercepts from the graphical representation of a quadratic function to determine and confirm its factors.

A.4c3  Confirm algebraic solutions to quadratic equations, using a graphing calculator.

### KEY VOCABULARY

literal equation (formula), expression, equation, properties of real numbers, properties of equality, quadratic equation, quadratic function, quadratic expression, roots, zeros, linear equation, system, substitution, elimination, ordered pair, coordinate, intersection, intercepts, solution, infinite, parallel, coincide, simultaneous

Updated: Oct 27, 2017