College Algebra Math 1111 Exam 2
Review questions and answers
What can a Linear Function Equation be written as? - answersf(x) = ax + b or f(x) = mx
+ b.
The formula for a quadratic function is different from that of a linear function because it
contains an x^2 term.
Examples:
f(x) = 3x^2 + 3x + 5 and g(x) = 5 - x^2 are not linear equations because of the ^2's.
What is the Quadratic Function Equation? - answersThe "a" in f(x) is called the Leading
Coefficient.
What is a Parabola? - answersThe graph f(x) is called a Parabola.
Examples:
f(x) = 2x^2 - x + 1 (Opens Upward because positive. a>0.)
g(x) = -x^2 + 3x -5 (Opens Downward because negitive. a<0.)
The highest (Absolute Max)/lowest (Absolute Min) point is called the Vertex.
What is the Vertex Form? - answersParabola graph of f(x) = a (x-h)^2 + k with a not
equal to 0; vertex (h,k). For the Vertex, h is always the opposite and k is what is
displayed.
This formula is known as the Standard Form of the Parabola.
How do you make a Perfect Square? - answers
What is Completing the Square? - answersAs a Quadratic Expression: x^2 + kx +
(k/2)2.
As a Perfect Square Trinomial: x^2 + kx + (k/2)^2 = (x+k/2)^2.
Completing the Square Example... - answersx^2 + 4x + 5
1. x^2 + 4x ____ + 5
2. 4/2. ALWAYS divide by 2! Then square the answer; 2^2 = 4. Now add AND THEN
ALSO subtract it.
, 3. (x^2 + 4x + 4) + 5 - 4
4. Now make it a perfect square!
(x + 2)^2 + 1.
This is the Standard Form - f(x) = a(x - h)^2 + k.
1(x+2)^2+1; 1 is a, 2 is h and 1 is k. Vertex is (-2,1) and it is going Upwards.
How can you Graph Quadratic Functions? - answersBy hand or by using a calculator. A
calculator is a good tool to check your answer by hand!
How do you find the Area of a Rectangle? - answers
What is an easier alternate formula to find the vertex? - answers
A Projectile is... - answers... anything you can throw.
What is the Square Root Property? - answers
How do you do a Quadratic Equation by Calculator? - answersUse Y^1 & Y^2 in your
Calc. Hit Graph, and then use the Intersection.
What is the Quadratic Formula? - answers
Factoring can be done by... - answers... trial and error.
What is the Zero-Product Property? - answersab=0 if and only if a=0 or b=0.
What does Area equal? - answers
Two important things to remember in math are... - answersPEMDAS and to be careful
with your signs!
The Discriminate Formula is... - answers
What are Complex Numbers? - answersA Complex Number is a number than can be
written as a + bi. A is Real and B is Imaginary.
>0 (is postive) - 2 distinct real sol.
>| (bottom line) ( is zero) - Two solutons, but same. So 1.
<0 (is negative) - No real solutions.
What are some Complex Numbers? - answers1 + 2i, -3i, 4, 3 - 11i, etc.
Every Real Number is a Complex Number (Ex. 4 --> 4+0i).
Review questions and answers
What can a Linear Function Equation be written as? - answersf(x) = ax + b or f(x) = mx
+ b.
The formula for a quadratic function is different from that of a linear function because it
contains an x^2 term.
Examples:
f(x) = 3x^2 + 3x + 5 and g(x) = 5 - x^2 are not linear equations because of the ^2's.
What is the Quadratic Function Equation? - answersThe "a" in f(x) is called the Leading
Coefficient.
What is a Parabola? - answersThe graph f(x) is called a Parabola.
Examples:
f(x) = 2x^2 - x + 1 (Opens Upward because positive. a>0.)
g(x) = -x^2 + 3x -5 (Opens Downward because negitive. a<0.)
The highest (Absolute Max)/lowest (Absolute Min) point is called the Vertex.
What is the Vertex Form? - answersParabola graph of f(x) = a (x-h)^2 + k with a not
equal to 0; vertex (h,k). For the Vertex, h is always the opposite and k is what is
displayed.
This formula is known as the Standard Form of the Parabola.
How do you make a Perfect Square? - answers
What is Completing the Square? - answersAs a Quadratic Expression: x^2 + kx +
(k/2)2.
As a Perfect Square Trinomial: x^2 + kx + (k/2)^2 = (x+k/2)^2.
Completing the Square Example... - answersx^2 + 4x + 5
1. x^2 + 4x ____ + 5
2. 4/2. ALWAYS divide by 2! Then square the answer; 2^2 = 4. Now add AND THEN
ALSO subtract it.
, 3. (x^2 + 4x + 4) + 5 - 4
4. Now make it a perfect square!
(x + 2)^2 + 1.
This is the Standard Form - f(x) = a(x - h)^2 + k.
1(x+2)^2+1; 1 is a, 2 is h and 1 is k. Vertex is (-2,1) and it is going Upwards.
How can you Graph Quadratic Functions? - answersBy hand or by using a calculator. A
calculator is a good tool to check your answer by hand!
How do you find the Area of a Rectangle? - answers
What is an easier alternate formula to find the vertex? - answers
A Projectile is... - answers... anything you can throw.
What is the Square Root Property? - answers
How do you do a Quadratic Equation by Calculator? - answersUse Y^1 & Y^2 in your
Calc. Hit Graph, and then use the Intersection.
What is the Quadratic Formula? - answers
Factoring can be done by... - answers... trial and error.
What is the Zero-Product Property? - answersab=0 if and only if a=0 or b=0.
What does Area equal? - answers
Two important things to remember in math are... - answersPEMDAS and to be careful
with your signs!
The Discriminate Formula is... - answers
What are Complex Numbers? - answersA Complex Number is a number than can be
written as a + bi. A is Real and B is Imaginary.
>0 (is postive) - 2 distinct real sol.
>| (bottom line) ( is zero) - Two solutons, but same. So 1.
<0 (is negative) - No real solutions.
What are some Complex Numbers? - answers1 + 2i, -3i, 4, 3 - 11i, etc.
Every Real Number is a Complex Number (Ex. 4 --> 4+0i).
