Quadratic
The form of a quadratic function
f(x)=ax2+bx+c (a≠ 0)
The form of polynomial
P(x)=anxn+an-1xn-1+...+a1x+a0
(an, an-1,..., a1, a0 are real numbers; an ≠ 0)
Circle Equation with center (h,k) and radius r
(x-h)2+(y-k)2=r2
Standard form of quadratic function
f(x)=a(x-h)2+k
If c is a zero of the polynomial P, then
(a) P(c)=?
(b) (x-c) is a ___ of P(x).
(c) c is a(n) __-intercept of the graph of P.
(a) 0
(b) factor
(c) x
Quadratic formula for ax2+bx+c=0
x= (-b ± √(b2-4ac))/2a
Find the mistake
Line 3 should be -a(b2/4a2)
Line 4 should be -(b2/4a2)
The end behavior of a polynomial with a positive and odd degree and a negative and even leading coefficient
odd degree and negative LC ->
y→-∞ , as x→∞
y→-∞ , as x→-∞
(x-y)2=?
x2-2xy+y2
The vertex of f(x)=5x2-30x+49
f(x)=5(x-3)2+4
vertex (3,4)
Find a formula for the polynomial of the smallest possible degree:
(x+3)(x+1)3(x-2)2
Composition
f(g(2)) = f(5) = 6
The vertex, min/max value of g(x)=-2x2+ 4x - 5
g(x)=-2(x-1)2-3
vertex (1,-3) a=-2 < 0 -> max value
x = -b/2a=1, f(1)=-3
True or False Asymptote
(a, b, c) T
(d) F
Equation of f(x)=x2 after these transformations:
- Stretch vertically by a factor of 2
- Shift downward 2 units
- Shift 3 units to the right
f(x)=2(x-3)2-2