Lesson 6 Closed Minded Practice Understanding

Ready

When we solve equations, we often set the equation equal to zero and then find the value of . Another way to say this is “find the value of when .” That’s why we call solutions to equations the zeros of an equation. Find the zeros for the given functions. Then mark the solution(s) as a point on the graph of the function.

1.

a.

Find the zero(s).

b.

Mark the solution(s) as a point on the graph of the function.

a positive linear function with the slope of 2 over 3 graphed on a coordinate plane x–5–5–5y555000

2.

a.

Find the zero(s).

b.

Mark the solution(s) as a point on the graph of the function.

a linear function with the slope of negative 4 over 3 graphed on a coordinate plane x111222333y111222333444000

3.

a.

Find the zero(s).

b.

Mark the solution(s) as a point on the graph of the function.

a positive linear function with the slope of 2 graphed on a coordinate plane x–1–1–1111222y–3–3–3–2–2–2–1–1–1111000

4.

a.

Find the zero(s).

b.

Mark the solution(s) as a point on the graph of the function.

a parabola with a vertex at the point (1,-20) going through the point (0,-15) x–1–1–1111222333y–20–20–20–10–10–10000

5.

a.

Find the zero(s).

b.

Mark the solution(s) as a point on the graph of the function.

a parabola opening up graphed on a coordinate plane with a point at (2.5,-25) x111222333444555y–20–20–20–10–10–10000

6.

a.

Find the zero(s).

b.

Mark the solution(s) as a point on the graph of the function.

a parabola opening down graphed on a coordinate plane x–4–4–4–3–3–3–2–2–2–1–1–1111222333y101010

Set

Identify the following statements as sometimes true, always true, or never true. If your answer is sometimes true, give an example of when it’s true and an example of when it’s not true. If it’s never true, give a counterexample.

7.

The product of a whole number and a whole number is a whole number.

8.

The product of an integer and an integer is an integer.

9.

The quotient of a whole number divided by a whole number is a whole number.

10.

The product of two rational numbers is a rational number.

11.

The product of two irrational numbers is an irrational number.

12.

The difference of a linear function and a linear function is an integer.

13.

The sum of a linear function and a quadratic function is a quadratic function.

Indicate if the statement is true or false. If it is false, find a counterexample to prove the claim is false. (Recall that a set of number is closed under an operation if it will always produce another number in the same set.)

14.

The set of irrational numbers is closed under addition.

15.

The set of integers is closed under addition and multiplication.

16.

The set of irrational numbers is closed under multiplication.

Go

Find the product of each pair of conjugates.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

Find the two complex solutions.

27.

28.

29.

30.