Chapter 5 –
5.1 Things I already know
1. Copy the objective.
2. Standard form of a quadratic equation y =
ax2+bx+c
What features make this equation quadratic?
(What do you think the ABC form of a quadratic
relation would be?)
3. How to graph a quadratic equation using a T
table and plotting points.
Graph y=x2+4x-5 (What do we call this type
of graph?)
4. How to use the quadratic formula to solve a
quadratic equation of the form
ax2+bx+c=0
Solve for x: x2+6x-2=0
5 How to factor a simple quadratic expression and
then to use the factored form to solve the equation
expression=0
6 Factor the left hand side and solve for x 2+3x10=0
5.2 Graphs of Quadratic Functions
1. Copy the objective.
2. Define parabola. The graph of y=x2-6x+8 is a
parabola. How do you know?
3. Define Vertex of a parabola
4. Define axis of symmetry of a parabola
5. Give an example of a parabola equation and
give the coordinates of the vertex and the equation
of the axis of symmetry.
6. Describe the procedure for completing the
square in complete English sentences.
Complete the square
y=x2-6x-3
7. Write the formula for the vertex form of a
parabola? What are the coordinates of the vertex?
Example 1:
Transform the equation by completing the square.
Write the coordinates of the vertex and 2 other
points and use these points to sketch the graph.
Y=2x2+12x –3
5.3 X intercepts and the Quadratic Formula
1. Copy the objective.
2. Memorize the quadratic formula
3. Use the quadratic formula to find the x
intercepts of the graph of
2x2+5x-7=2
4. Copy the definition of the discriminant. Using
3 different examples (one for each of the stated
conditions) show that the statements in the blue
box are true.
5. What does the discriminant value tell you about
the solutions of a quadratic equation?
6. What is the symmetric point of the y intercept
of a parabola?
Example 1: Solve 3x2-10x-2=0
.Example 2: Solve 2x2-3x+5=0
Example 3: y=x2-10x+4 Find the vertex, x
intercepts, y intercept and its symmetric
point. Use this information to sketch the
graph
7. Copy the formula for the x coordinate of the
vertex of a parabola. When you know the
x coordinate, how do you find the y
coordinate??
Example 4: y=3x2-6x-2
Use the shortcut formula to find the vertex of this
parabola.
5.4 Imaginary and Complex Numbers
1. Copy the objective.
2. Define imaginary number and give 3 examples
3. What does i represent? (Copy blue box on p.
189)
4. Write the number 40 in terms of i.
5. Copy blue box top of p. 190. Write the number
4x 2 in terms of i
6. Copy the definition of complex
 number and
restate in your own words. Give 3
examples.
 of complex conjugate and
7. Copy the definition
restate in your own words Write 3
examples of complex conjugate pairs
8. Describe in complete English sentences how to
graph a complex number on the complex
plane.
Example1: x2+2x+7=0
Solve the equation and check one of the
solutions by substitution (no calculators).
Example 2: 3x2+8x=9x-7
Solve the equation and check one of the solutions
by substitution (no calculators).
5.5 Evaluating Quadratic Functions
1. Copy the objective.
Example 1: f(x) = 2x2+3x-5
Find a) f(-4), b) x when f(x) =3 c) the x
intercepts
2. Does the function f(x)=2x2+8x-15 ever equal –
5? Does it ever equal –10? How do you know?
5.6 Equations of Quadratic Functions and
graphs
1. Copy the objective.
Example 1: find the quadratic equation passing
through the points (1,2) (-2,23) (3,8)
Example 2: Find the equation of the graph
passing through the three points (0,7) (1.6)
(-3,34)
Example 3: find the quadratic equation with a
vertex at (-2,3) and passing through the
point (4,12)
5.7 Quadratic and Linear Functions as
Mathematical Models
1. Copy the objective.
2. The cost of square ice cream cakes is a
quadratic function of the side length. The costs ae
Small (6 inch side)
$10.60
Medium (8 inch side)
$14.40
Large (12 inch side)
$24.40
a) What would the price of an 16 inch side cake
be?
b) Suppose they sold a mini cake (3 inch side),
what would the price be?
c) The price intercept is the price when the side
length is 0. What is the price intercept?
Why is it not equal 0?
d) Use the discriminant to show that there are no
side lengths for which the price is 0.
e)Show that a linear function does not fit the
data.
f) Find the vertex and use it to help you draw
the graph.