Chapter 9 Notes Alg. 1H

9-A1 (Lesson 9-3) “Solving Quadratic Equations by Finding the Square Root and Completing the Square” p. 486*Calculator

Find the Square Root: take the square root of ______.

Ex:

Solve by finding square roots. Round to the nearest tenth.

√1) 2) 3)

Steps for Completing the Square:

  1. If necessary, divide both sides by ______.
  2. Isolate the ______terms.
  3. Divide the coefficient of ____ by ____; ______it.
  4. Add that number to ______of the equation.
  5. ______the trinomial as ______or ______.
  6. Take the ______of each side.
  7. ______for x.

Examples:

Solve by completing the square. Leave answers in radical form where necessary.

4) 5)

Solve by completing the square. Round answers to the nearest tenth where necessary.

6) 7)

9-A3/4 (Lesson Heath 12.4 and Glencoe 9-1)“Graphing Quadratic Functions” (Vertex Form)

Heath p. 639-642

Standard Form:

  • Completed Square Form (Vertex Form):
  • Parabola:
  • Vertex:
  • Minimum:
  • Maximum:
  • Axis of symmetry: the line that divides a ______into 2 halves
  • Equation:
  • To sketch a parabola:

1)Find the ______.

  • Use the Completed Square/Vertex to find the values of h and k
  • Write the Vertex as an ordered pair:

2)Make a ______of values.

  • Choose at least ______additional values of ______.
  • 2 values ______than the x-value of the vertex and 2 values that are ______.
  • ______to find y values and complete the table.

3)Plot the ______and draw a ______.

1.

vertex: ( , )

x
y

2.

vertex: ( , )

x
y

3.

vertex: ( , )

x
y

4. Physics Problem Example: (Use graphing to solve)

Miranda throws a set of keys up to her brother, who is standing on a balcony 38 ft. above the ground. She throws with a velocity of 40 ft/sec. and her hand is 5 ft. off the ground. How long does it take the keys to reach their highest point? Will her brother be able to catch the keys?

9-A5 (Lesson 9-2)“Solving Quadratic Equations by Graphing & Finding Roots”

p. 480-483

Quadratic Equation: (standard form)

  • Roots: ______
  • Zeros: ______
  • Check: by ______

1.

vertex: ( , )

x
y

2.

vertex: ( , )

x
y

3.

x
y

vertex: ( , )

  • Use Factoring first to determine how many times the graph ______the ______.

4.

x
y

Factor:

Intersections:______Roots: ______

  • Integral Roots:
  • If roots aren’t integers,______; write solution as a compound ______

5.

x
y

9-A6 Notes Quadratic Word Problems *calculator Alg. 1H

EX 1: The path of a ball kicked against a wall (the y axis is the wall) follows the path y = x2 + x + 4, where y is the height of the ball in feet, and x is the horizontal distance (in feet) from the wall.

1

Notes Ch.9 Alg. 1H

A) How high is the ball at its maximum height?

B) How far above the ground does the ball hit the wall? (The y axis represents the wall.)

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Notes Ch.9 Alg. 1H

EX 2: In the diagram below, the backboard is located on the y-axis and the hoop is located at the point (1,10). A basketball thrown toward the hoop follows the path y = ־.45x2 + 3.2x + 6.2 where x and y are measured in feet.

1

Notes Ch.9 Alg. 1H

A) When the ball was at its highest point, what was its horizontal distance from the backboard? (Round to two decimal places.)

B) At its highest point, how far off the ground was the basketball?

1

Notes Ch.9 Alg. 1H

EX 3: How deep is the pond given by the equation y = x2 + 2x – 5?

Pythagorean Theorem:

9-A8 (Lesson 9-4A) “Solving Quadratic Equations by Using the Quadratic Formula”CALCULATOR p. 493-497

  • Quadratic Formula:

Used to solve Quadratic Equations:

Read Ex. 1

1

Notes Ch.9 Alg. 1H

√1A. ..

a =

b =

c =

√1B.

a =

b =

c =

1

Notes Ch.9 Alg. 1H

C.) A roofer tosses a piece of roofing tile from a roof onto the ground 30 ft below. He tosses the tile with an initial velocity of 10 ft. per second. How long does it take the tile to hit the ground?

9-A9 (Lesson 9-4B) “Using the Discriminant” p. 496-497

  • Discriminant: the ______(expression inside the radical symbol); part of the ______formula

Three possibilities for the discriminant:

No Solution One Solution Two Solutions

(Does not intersect the x-axis) (Vertex is on the x-axis) (Intersects x-axis at two points)

Read Ex. 3 p. 496

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Notes Ch. 9 Alg. 1H

√3A. B. C.

  • When the discriminant is a perfect square, the solutions will be ______numbers

9-A11“Derivation of Quadratic Formula and Choosing a Method”

  • Solve the following by completing the square:
  • This is called “the Derivation of the ______”

Which method should you choose to solve ?

(in order of preference and efficiency!)

Choice

/

Method

/ When to Use / Lesson
1 / When b = 0

To solve ______

2 / When easily ______
3 / Best when ______and b is an ______number
4 / Any quadratic equation; gives ______solutions
Visual model / Any quadratic equation; gives ______solutions

9-A12 “Exponential Functions” p. 502-505

  • Standard Form:
  • The variable is:

1. Graph: and

x / y
x / y

2. Graph:

x / y
x / y
x / y

3. Graph:

x / y
x / y
x / y

4. Graph:

x / y
x / y
x / y

Transforming a Graph of an Exponential Function:

Change in Function /

Type of Change

/ Positive or Negative / Change in Graph
b
x

a

Is it necessary to make a table when you already know the transformation?

1

Notes Ch. 9 Alg. 1H