Introduction to Quadratics
Standard Form
y=ax2+bx+c
What is Standard Form?
Well standard form is a trinomial that looks like this..
y=ax2+bx+c
How to find the Zeros/X-intercepts from Standard Form
To find zeros easily from Standard Form, you should use the Quadratic Formula. The Quadratic Formula can be used in place of factoring. It is much easier and a lot less messier.
Standard Form
Quadratic Formula
is equal to
Consider This...
y=ax2+bx+c
0=2x2-6x+1
1. Find your 'a' value, 'b' value, and 'c' value
a=2 b=-6 c=1
2. Now sub in these numbers into the quadratic formula
On one side x is On the other side x is equal to
equal to 6+5.29/4 6-5.29/4
x = 6 + 5.29 /4 x= 6-5.29 /4
x=2.8 x=0.18
By the end you should have two x intercepts. In this specific example our x intercepts or other know as our zeros are 2.8 and 0.18 .
LETS FIND AXIS OF SYMMETRY OR THE X VALUE OF THE VERTEX
To find the axis of symmetry you can use this simple formula.....
-b/2a
Just sub in the values for "b" and "a", in this case b is equal to 6 ( becuase -b and -6 = positive 6) and "a" it is equal to 2.
6/2(2)=1.5
Optimal Value
Now to find your optimal value sub in you x-value into your original equation and solve!
y= 2x^2-6x+1
y= 2(1.5)^2-6(1.5)+1
y=3^2-9+1
y=3^2-10
y=9-10
y=-1