Math Unit 2 Test

Question 1

The graph of a quadratic is called a…

Answer 1

PARABOLA

Question 2

The ? of a parabola is the point on the graph with the greatest y-coordinate if the graph opens down or the least y-coordinate if the graph opens up

Answer 2

VERTEX

Question 3

When the quadratic relation is used to model a situation, the y-coordinate of the vertex corresponds to an ? (Maximum/Minimum) value.

Answer 3

OPTIMAL

Question 4

Depending on the ? of the parabola, you will either have a ? or ? value of the equation

Answer 4

DIRECTION OF OPENING
MAXIMUM or MINIMUM

Question 5

The ? value is always the y-value of the Vertex

Answer 5

MAXIMUM/MINIMUM

Question 6

standard form + characteristics

Answer 6

y = a^2 + bx + c
- c is the y-intercept
- ‘a’ is positive it OPENS UP
- ‘a’ is negative it OPENS DOWN

Question 7

vertex form + characteristics

Answer 7

y = a(x-h)^2 + k
- (h,K) is the VERTEX
- ‘a’ is positive it OPENS UP
- ‘a’ is negative it OPENS DOWN

Question 8

factored form + characteristics

Answer 8

y = a(x-r)(x-s)
- ‘r’ and ‘s’ are the x-intercepts
- ‘a’ is positive it OPENS UP
- ‘a’ is negative it OPENS DOWN

Question 9

Maximum if ‘a’ is …

Answer 9

NEGATIVE

Question 10

Minimum if ‘a’ is …

Answer 10

POSITIVE

Question 11

Maximum/Minimum Value is …

Answer 11

‘k’

Question 12

Equation of Axis of Symmetry…

Answer 12

x = h

Question 13

Steps to Completing the Square:

Answer 13

1. Put brackets on the first 2 terms
2. Factor out the value in front of x2
3. Take ½ of the value in front of x and Square it
4. Add AND Subtract that value into the bracket
5. Remove the Subtracted value from the bracket, (multiply by ‘a’ when removing)
6. Factor the trinomial bracket (it’s ALWAYS a Perfect Square Trinomial)

Question 14

Revenue =

Answer 14

Cost x Number Sold

Question 15

Area =

Answer 15

L X W

Question 16

Steps for Real Life Applications of Quadratic Functions

Answer 16

1. Create a let statement
2. Ensure that there’s only one variable
3. Sub that equation in
4. Foil until you have a Quadratic Function
5. Complete the square
6. `Max/Min is K, X will be the ticket price or width

Question 17

Solving a Quadratic Equations means to

Answer 17

find the unknown variable.

Question 18

Steps to Solving Quadratic Equations by Factoring and Quadratic Formula

Answer 18

1. Place all numbers and variables on one side of the equation = 0
2. Strategies for solving Quadratic Equations
   - Factoring
   - Quadratic Formula

Question 19

Quadratic Formula

Answer 19

x = -b +/- √ b^2 - 4ac / 2a

Question 20

Vertex form - (h,k)

Answer 20

y = a(x-h)^2 + k

Question 21

Factored form - x-intercepts r & s

Answer 21

y = a (x-r)(x-s)

Question 22

My steps to Finding the Quadratic Equations

Answer 22

1. Examine the question -
   a. if you’re given a vertex (h,K) and a point (x,y) solve using vertex form
   b. If you’re given the x-intercepts (r and s) and a point (x,y) solve using factored form
2. Sub everything else in
3. Solve for a
4. Rearrange the Equation

Question 23

Nature of Roots =

Answer 23

How many Points of Intersection (x-intercepts) does the Quadratic Equation have?

Question 24

Discriminant =

Answer 24

b^2 - 4ac

Question 25

When b^2 - 4ac > 0

Answer 25

2 x-intercepts

Question 26

When b^2 - 4ac = 0

Answer 26

1 x-intercept

Question 27

When b^2 - 4ac < 0

Answer 27

0 x-intercepts

Question 28

Steps for The Discriminant and the Nature of Roots

Answer 28

1. Use the discriminant and plug in the numbers
2. If asked for k do the same then solve for K

Question 29

Steps for Applications of Quadratic Equations

Answer 29

1. Write let statement for what you are trying to find
2. Create a (Quadratic) Equation
3. Solve for the unknown variable using:
   a) Factoring
   b) Quadratic Equation

Question 30

A linear function and a quadratic function can intersect at a ? of ? points

Answer 30

MAXIMUM
2

Question 31

Steps for Intersection of Linear and Quadratic Functions:

Answer 31

1. Rewrite the LINEAR equation in the form of y=mx+b
2. Substitute the LINEAR equations into the QUADRATIC equation (for the y variable)
3. Solve for the unknown variable (Factoring or Quadratic formula)
4. Substitute the found variable into either original equation (the Linear is usually a nice option) to find the other variable
5. State the Point(s) of Intersection