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Algebra Name:

Assignment Sheet Date:

Period:

Quadratic equations and functions

(1) Page 507 - 508 #23 - 75 Left

(2) Page 507 - 508 #26 - 77 Right

(3) Page 521 #5 - 13

(4) Page 521 #21, 25, 29; Page 522 #44 - 56 Left graph

paper needed

(5) Page 521 #23, 27, 31; Page 522 #44 - 58 Right

Graph paper needed

(6) Page 529 #3 - 14 Graph paper

(7) page 529 - 530 #18 - 20, #21 - 36 left graph

paper needed ****Quiz Tomorrow****

(8) Page 536 - 537 #23, 26, 32, 35, 38, 44, 47, 50, 53, 56, 59

(9) Page 536 - 537 #25, 28, 34, 37, 40, 26, 49, 55, 58

(10) Page 544 #3 - 8, #18 - 20

(11) page 544 - 545 #9 - 17, 24 ****Quiz

Tomorrow****

(12) chapter review for test tomorrow

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9.1 Solving Quadratics by Square Roots (include cubic equations up to 125) (I,E/2)

All positive real numbers have two square roots: a ___________________ square root (or principal

square root) and a ___________________ square root. Square roots are written with a radical symbol

√ . The number or expression inside a radical symbol is the ___________________.

Meaning Positive square root Negative square root The positive and

negative square roots

Symbol √ √ √

Example √ √ √

Numbers whose square roots are integers or quotients of integers are called ______________________. The square roots of a number that are not perfect squares must be written using the radical symbol or approximated. These numbers are part of the set of irrational numbers. An _______________________ is a number that cannot be written as a quotient of two integers (aka fraction). A _______________________ equation is an equation that can be written in the following ___________________ form.

In standard form, a, is the ____________________ coefficient. E1) Evaluate the expression

a. √ b. √ c. √ d. √ e. √

P1) Evaluate the expression

a. √ b. √ c. √ d. √ e. √

E2) Evaluate the expression. Use a calculator if necessary and round to the nearest hundredth.

a. √ b. √ c. √ d. √

P2) Evaluate the expression. Use a calculator if necessary and round to the nearest hundredth.

a. √ b. √ c. √ d. √

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E3) Evaluate √ when a = 1, b = -2 and c = -3.

P3) Evaluate √ when a = 7, b = 8 and c = 1.

E4) Evaluate (with a calculator and round answer to the nearest hundredth) √

P4) Evaluate (with a calculator and round answer to the nearest hundredth) √

E5) Solve the equation (exact answers in simplest radical form)

a. b. c. d.

P5) Solve the equation (exact answers in simplest radical form)

a. b. c. d.

E6) Solve the equation.

a.

P6) Solve the equation.

a.

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9.3 Graphing Quadratic Functions (I,E/3)

A _______________________________ function is a function that can be written in the __________________________

form:

Every quadratic function has a U-shaped graph called a _______________________________. If the leading

coefficient a is positive, the parabola opens up. If the leading coefficient is negative, the parabola

opens down in the shape of an upside down U.

The __________________________ is the lowest point of a parabola that opens up and the highest point of a

parabola that opens down.

The line passing through the vertex that divides the parabola into two symmetric parts is called the

_________________________________________________. The symmetric parts are mirror images of each other.

The axis of symmetry is the vertical line:

The vertex is found on the axis of symmetry.

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STEPS:

1. (A of S) Find the axis of symmetry (

).

2. (Table) Make a table with the vertex in the middle and at least two points to the left and

right

3. (Graph) Plot the points

E1) Sketch the graph of

A of S (VUX) Table Graph

x Y

P1) Sketch the graph of

A of S (VUX) Table Graph

x Y

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E2) Sketch the graph of

A of S (VUX) Table Graph

x Y

P2) Sketch the graph of

A of S (VUX) Table Graph

x Y

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9.4 Solving Quadratic Equations by Graphing (I,E/2)

Solving Quadratic Equations Using Graphs

Steps:

1. Write the equation in the form

2. Write the related function

3. Sketch the graph of the function.

4. The solutions, or ______________, of are the x-intercepts.

E1) Solve

algebraically. Represent your solutions as the x-intercepts of a graph.

Solve by Square Roots

Write the related function of this equation ( )

Table Graph

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Steps:

1. Write the equation in the form

2. Write the related function

3. Sketch the graph of the function.

4. The solutions, or ______________, of are the x-intercepts.

P1) Solve algebraically. Represent your solutions as the x-intercepts of a graph.

Solve by Square Roots

Write the related function of this equation ( )

Table Graph

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Steps:

1. Write the equation in the form

2. Write the related function

3. Sketch the graph of the function.

4. The solutions, or ______________, of are the x-intercepts.

E2) Solve algebraically. Represent your solutions as the x-intercepts of a graph.

Solve by ZPP

Write the related function of this equation ( )

Table Graph

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Steps:

1. Write the equation in the form

2. Write the related function

3. Sketch the graph of the function.

4. The solutions, or ______________, of are the x-intercepts.

P2) Solve algebraically. Represent your solutions as the x-intercepts of a graph.

Solve by ZPP

Write the related function of this equation ( )

Table Graph

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9.5 Solving Quadratic Equations by the Quadratic Formula (I,E/2)

The Quadratic Formula

The solutions of the quadratic equation are

√

You can read this formula as “x equals the opposite of b, plus or minus the square root of b squared

minus 4ac, all over 2a.”

Steps:

1. Plug it in

a. Plug the values of a, b and c into the quadratic formula

2. Break it down

a. Break down the radical

3. Reduce

a. Simplify the solution

E1) Solve: P1) Solve:

E2) Solve: P2) Solve:

E3) Find the x-intercepts of the graph P3) Find the x-intercepts of the graph

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Discriminant

9.6 Applications of the Discriminant (I,E/2)

In the quadratic formula, the expression inside the radical is the ______________________.

√

The number of solutions of a quadratic equation

If , then the equation has ___________ solutions.

If , then the equation has ___________ solutions.

If , then the equation has ________________________ solutions.

E1) Find the value of the discriminant and use the value to tell if the equation has two solutions, one

solution, or no solution.

a. b. c.

P1) Find the value of the discriminant and use the value to tell if the equation has two solutions, one

solution, or no solution.

a. b. c.

E2) Use the related equation to find the number of x-intercepts of the graph of the function.

a. b. c.

P2) Use the related equation to find the number of x-intercepts of the graph of the function.

a. b. c.