Mr. Stump Algebra II W/ Trig
Name____________________
Unit 3 Quadratics Review Guide
Date____________ Period ___
Concepts Covered:

Quadratic Equations in Vertex Form

Quadratic Equations in Standard Form

Converting Between Vertex & Standard Form

Finding Solutions in Vertex Form & Standard Form

Finding Zeros of a Quadratic by Factoring

Finding Zeroes of a Quadratic by Quadratic Formula

Writing Quadratic Equations from zeros/roots

Determining types of solutions from the Discriminant

Operations with Complex Numbers

Graphing Quadratic Equations given an equation

Finding the Equation of a Parabola of a Graph
Concepts not covered yet:
i.

Systems of linear/linear, linear/parabolic, parabolic/parabolic equations

Quadratic Inequalities

Word Problems
In vertex form, write the general equation of a quadratic function
__________________
In standard form, write the general equation of a quadratic function
________________
ii.
Convert the following equations from vertex form to standard form:
y = (x-2)2 + 3
y = -2(x+2)2 – 4
y = _________
y = ___________
y = a(x-h)2 + k
y = ___________
Write the relationships between the forms as follows:
Vertex  Standard
Standard Vertex
A=
a=
B=
h=
C=
k=
Use the relationships to convert the following from standard to vertex:
iii.
y = -x2 - 4x -2
y = 2x2 - 4x + 4
y = ax2 + bx + c
y = ___________
y = ___________
y = ___________
Find the solution(s) to the quadratic equation y = -2(x+2)2 – 4 for the following; Write
your solutions as ordered pairs.
a. x = 3
b. x = 5
c. y = -4
d. y = -12
e. y = 0
Use either factoring and/or the quadratic formula to find the solution(s) to the quadratic
equation y = 2x2 - 4x + 4 for the following; Write your solutions as ordered pairs.
a. x = 3
b. x = 5
c. y = 4
d. y = 2
iv.
Factor the following equations to find the zeros of function.
a. y = x2 +2x + 1
b. y = 2x2 + 3x - 2
c. y = 4x2 - 4x – 3
Use the Quadratic formula to find the zeros of the function
a. y = x2 +2x + 1
b. y = 2x2 + 3x - 2
c. y = 4x2 - 4x - 3
v.
Determine the number and type of solutions (real & imaginary) to the following quadratic
equations by examining the discriminant.
a. 0 = x2 +2x + 1
b. 0 = 2x2 + 3x - 2
c. 0 = -2x2 - 4x - 3
vi.
Perform the following operations with complex numbers.
a. (-5 + 3i) + (2 – 6i)
b. (-5 + 3i) - (2 – 6i)
c. (-5 + 3i) x (2 – 6i)
d. |-5 + 3i|
vii.
List all Key components of the parabolas of the following and then graph.
a. y = (x-2)2 + 3
viii.
Find the equation of the following parabolas.
y = _____________
ix.
b. y = 2x2 - 4x + 4
y = _____________
Use the following three points to determine the quadratic equation that fits all three.
(-1,-10),(0,-4),(1,-2)
x.
Find the solutions to the following systems of equations by algebraically then check your
answer by graphing.
y = 2x + 1
y = 2x + 1
y = 2x2 - 4x + 4
y = 4x + 3
y = 2x2 - 4x + 4
y = -x2-6x-7