ALGEBRA: Quadratic Equations in Pasadena
Pasadena Students Excel in Algebra with the Help of A Plus In Home Tutors.
Algebra students are quickly discovering methods to solve those seemingly complicated quadratic equations.
ALGEBRA: The Basics
What is a Quadratic Equation?
The name Quadratic comes from “quad,” meaning square because the variable gets squared.
A Quadratic is an equation of standard form, that involves only two things besides numbers: a variable and a square of this variable.
• a, b and c are known as values. a can’t be 0.
• “x” is the variable
Here are some more examples of standard form Quadratic Equations:
In this one a=2, b=5 and c=3
In this one a=1, b= -3 and c=0
The “solutions” to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions. They are also called “roots” or sometimes “zeros.”
How to Solve Quadratic Equations
Using fun, interactive ways, tutors will demonstrate 3 main methods to find quadratic solutions:
1. Factoring
2. Completing the Square
3. Using the Quadratic Formula
Of these three methods, the Quadratic Formula is the most common and most reliable.
Quadratic Formula:
Simply plug in the values of a, b and c, and do the calculations.
Some of the symbols in this formula may appear familiar.
The ± means there are TWO answers:
Here you see why you can get two answers:
But sometimes you don’t get two real answers. A Plus In Home Tutors will take the next step to explain what this means and how to proceed when test taking.
Discriminant
Do you see b2 – 4ac in the formula above? It is called the Discriminant because it can “discriminate” between the possible types of answers:
• when b2 – 4ac is positive, you get two Real solutions
• when it is zero you get just ONE real solution (both answers are the same)
• when it is negative you get two Complex solutions
Using the Quadratic Formula to Solve the Equation
Example: Solve 5x² + 6x + 1 = 0
Coefficients are: a = 5, b = 6, c = 1
Quadratic Formula: x = [ -b ± √(b2-4ac) ] / 2a
Put in a, b and c: x = [ -6 ± √(62-4×5×1) ] / (2×5)
Solve: x = [ -6 ± √(36-20) ]/10
x = [ -6 ± √(16) ]/10
x = ( -6 ± 4 )/10
x = -0.2 or -1
Answer: x = -0.2 or x = -1
And you can see them on this graph.
Check -0.2: 5×(-0.2)² + 6×(-0.2) + 1
= 5×(0.04) + 6×(-0.2) + 1
= 0.2 -1.2 + 1
= 0
Check -1: 5×(-1)² + 6×(-1) + 1
= 5×(1) + 6×(-1) + 1
= 5 – 6 + 1
= 0
Once a Pasadena Algebra student understands how to recognize and solve quadratic equations with the help of a tutor,
they will become more confident in their problem-solving abilities as well as their test-taking skills.
Every student will benefit from the tutoring experts of A Plus In Home Tutors.