Algebra 1

Unit 4: Expressions and Equations

Cluster

Write expressions in equivalent forms to solve problems.

A.SSE.3: Algebra – Seeing Structure in Expressions

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a) Factor a quadratic expression to reveal the zeros of the function it defines.

Essential Skills

and Knowledge:

Ability to connect the factors, zeros, and x-intercepts of a graph

Ability to use the Zero-Product Property to solve quadratic equations

Ability to recognize that quadratics that are perfect squares produce graphs which are tangent to the x-axis at the vertex

Drill:Find the numbers represented by the symbols that satisfy the given conditions:

* = -3

+ = -2

Introductory Activity:

Algebra Tiles Game

Rules: Green side is positive, yellow side is negative.The big square is x2, the stick is x, the little square is 1.A pair of the same shape but different colors will cancel each other out.

Each team will receive a pack with these materials.

I will write an expression on the board and I want you to form a rectangle using all the pieces representing the expression.

You can only add sticks, and they should be in pairs.

Q: What property should this pair of sticks have and why?

Here is an example of a rectangle:

What expression does this rectangle represent?

x2 + 2x – 15

The Expression: x2 – 2x – 3

Remember the Drill?Find the numbers represented by the symbols that satisfy the given conditions:

* = -3

+ = -2

I. Factoring an Expression:

Factor: 1) x2 – 2x – 3

I. Factoring an Expression:

Factor: 2) x2 – 6x + 9

II. Solving a Quadratic Equation:

Zero Factor Law:

If a*b = 0, then either a = 0 or b = 0.

Solve:(x + 3)(x – 5) = 0

II. Solving a Quadratic Equation:

Solve:1) x2 – 2x – 3 = 0

II. Solving a Quadratic Equation:

Solve:2) x2 – 6x = –9

III. Finding the Zeros of a Quadratic Function:

1) y = x2 – 2x – 3

Graph:y = x2 – 2x – 3

x

y

III. Finding the Zeros of a Quadratic Function:

2) f(x) = x2 – 6x + 9

Graph:f(x) = x2 – 6x + 9

x

y

Closure: Exit TicketFill in the blanks:

1) The solutions to a quadratic equation are the ___________ of the corresponding quadratic function.

2) The lowest (or highest) point in a parabola is called a _________.

Quadratic VideosTeach Me How To Factor

Quad Solve!!!