#### Math - 2017-18

# 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.4The student willsolveb) quadratic equations in one variable algebraically;

**Bloom's Level:** Apply

*Adopted: 2009*

### 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.

2016 VDOE Curriculum Framework - AI.4 Understanding

· 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.4c_{1} **Solve**
quadratic equations.

·
A.4b_{1 }**Solve**
quadratic equations in one variable algebraically. Solutions may be rational or irrational.

·
A.4b_{2 }**Apply**
the properties of real numbers and properties of equality to **simplify** expressions and **solve** equations.

A.4c_{2} **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.7bcd_{1 }**Identify**
the domain, range, zeros, and intercepts of a function presented algebraically
or graphically.

·
A.7cd_{1 }**Use**
the *x*-intercepts from the graphical
representation of a quadratic function to **determine**
and **confirm** its factors.

A.4c_{3} **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*