Math: Quadratic Relationship
Can't we just factor and find all the zeroes, axis of symmetry, optimal value?
Yes, you can factor and find all those but what about the equations you can't factor?
You would have to use the quadratic formula to find the x-intercepts.
Example on quadratic formula:
Standard form equation: y=x²-8x+12
x=-b±√b²-4ac/2a
x=-(-8)±√(-8)²-4(1)(12)/2(1)
x=8±√64-48/2
x=8±√16/2
x=6 and x=2
To find the A.O.S. do the same thing you did in factored form(as you might have noticed you keep doing similiar steps in every form):
A.O.S.=6+2/2
A.O.S.=8/2
A.O.S.=4
For the optimal value just sub 4 into the equation:
y=x²-8x+12
y=(4)²-8(4)+12
y=16-32+12
y=-4
Now you have the A.O.S. and the optimal value which means you also have the vertex.
The standard form equation (as mentioned many times) is:
ax²+bx+c
The quadratic formula is:
x=-b±√b²-4ac/2a
Basically to find the x-intercept(s)(there may be more then 1 or 0) you substitute the "a", "b", and "c" in the quadratic formula and use your calculator to find the answer.
If you're having difficulties then ask your teacher on how to use your calculator.