SOLUTION: In your own words, explain how to solve a quadratic equation using the quadratic formula. Demonstrate the process with your own example.

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Question 439755: In your own words, explain how to solve a quadratic equation using the quadratic formula. Demonstrate the process with your own example.




Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic+formula will calculate the solutions of any quadratic+equation.
A quadratic equation is an equation that can be written as
ax%5E2+%2B+bx+%2B+c where a ≠ 0
In other words, a quadratic+equation+must+have a squared term as its highest power.
The solution of a quadratic+equation is the value of x when you set the equation equal to zero,
or when you solve the following general equation: 0+=+ax%5E2+%2B+bx+%2B+c
Given a quadratic equation: ax%5E2+%2B+bx+%2B+c
The quadratic formula below will solve the equation for zero
The quadratic formula is : x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Example:
Quadratic Equation: y+=+x%5E2+%2B+2x+%2B+1 where
a+=+1
b+=+2
c+=+1
Using the quadratic formula to solve this equation just substitute a,b, and c into the general formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+
x+=+%28-2+%2B-+sqrt%28+4-4+%29%29%2F2+
x+=+%28-2+%2B-+sqrt%28+0+%29%29%2F2+

x+=+%28-2+%2B-0+%29%2F2+
x+=+-2+%2F2+
x+=+-1+

here is the graph of y+=+x%5E2+%2B+2x+%2B+1 and its solution:

+graph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+%2B+2x+%2B+1%29+

so, as you can see, this quadratic function has only one solution (the parabola is touching x-axis at -1)