Use Graphs to Solve Quadratic Equations
Key Questions

Take the whole function and set it equal to zero, then just solve it like you would a normal equation.

Answer:
A complex number '
#alpha# ' is called a solution or root of a quadratic equation#f(x) = ax^2 + bx + c #
if#f(alpha) = aalpha^2 + balpha +c = 0# Explanation:
If you have a function 
#f(x) = ax^2 + bx + c #
and have a complex number #alpha# .If you substitute the value of
#alpha# into#f(x)# and got the answer 'zero', then#alpha# is said to be the solution / root of the quadratic equation.There are two roots for a quadratic equation .
Example :
Let a quadratic equation be 
#f(x) = x^2  8x + 15# The roots of it will be 3 and 5 .
as
#f(3) = 3^2  8*3 + 15 = 9  24 +15 = 0# and#f(5) = 5^2  8*5 + 15 = 25  40 +15 = 0# . 
Let us look at the following example.
Solve
#2x^2+5x3=0# for#x# .(Be sure to move all terms to the lefthand side so that you have zero on the righthand side.)
Step 1: Go to "Y=" and type in the quadratic function.
Step 2: Go to "WINDOW" to set an appropriate window size.
Step 3: Go to "CALC", and choose "zero".
Step 4: It will say "Left Bound?", so move the cursor to the left of the zero and press "ENTER".
Step 5: It will say "Right Bound?", so move the cursor to the right of the zero and press "ENTER".
Step 6: It will say "Guess?", then move the cursor as close to the zero as possible and press "ENTER".
Step 7: The zero (
#X=3# ) is displayed at the bottom of the screen.Step 8: Repeat Step 37 to find the other zero (
#X=0.5# ).
I hope that this was helpful.

If you are solving the quadratic equation of the form
#ax^2+bx+c=0# ,and the graph of the quadratic function
#y=ax^2+bx+c# is available, then you can solve the quadratic equation by finding the xintercepts (or zeros) of the quadratic function.
I hope that this was helpful.
Questions
Quadratic Equations and Functions

Quadratic Functions and Their Graphs

Vertical Shifts of Quadratic Functions

Use Graphs to Solve Quadratic Equations

Use Square Roots to Solve Quadratic Equations

Completing the Square

Vertex Form of a Quadratic Equation

Quadratic Formula

Comparing Methods for Solving Quadratics

Solutions Using the Discriminant

Linear, Exponential, and Quadratic Models

Applications of Function Models