Study Pages. MAT170 SPRING 2009 Material for 1 st Quiz. How to “complete the Square” for f (x) = 3x 2 + 27x - 24 :. 1. Move anything w/o an x to the left f(x) + 24 = 3x 2 + 27x 2. Make the number in front of x 2 equal to 1 (f(x) + 24) /3 = x 2 + 9x
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MAT170 SPRING 2009
Material for 1st Quiz
1. Move anything w/o an x to the leftf(x) + 24 = 3x2 + 27x
2. Make the number in front of x2 equal to 1(f(x) + 24)/3 = x2 + 9x
3.Take the number in front of x, divide by 2 and then square the result. (9/2)2
4. Add the result of step 3 to both sides. (f(x) + 24)/3 + (9/2) 2 = x2 + 9x + (9/2)2
5.Factor the right side. (f(x) + 24)/3 + 20.25 = [x - (9/2)]2
6. Move everything back to the right and now you have the standard quadratic function equation. f(x) = 3[x - (9/2)]2 – 84.75
What is meant by an EVENfunction?
f(x) = f(-x)
-f(x) = f(-x)
f(x) = a(x-h)2+k am0
The graph of f is a parabola
with vertex at point (h,k)
if a>0, it opens UPward;
if a<0, it opens DOWNward
=(-b , c-b2) 2a 4a
X= -b kpb2-4ac
For standard quadratic equations:
ax2 + bx + c = 0 am0
Will reflect around the X axis
Will reflect around the Y axis
p-1 = i and i2 = -1
Divide the exponent by 4
If it divides evenly by 4, then the answer is 1.
The repeating pattern is:
-1, -i, 1, i
Fora+bi, it isa-bi
Multiply both numerator and denominator
by the complex conjugateof the denominator.
4-5i = (4-5i)(4+5i)