QUADRATICS
In the quadratic
f(x)=(x−4)^2−3
, what is the vertex?
(4,−3)
What is the degree of
f(x)=−5x^4+2x^2−1
4
Divide the polynomials.
(x^3-1) ÷ (x-1)
x^2+x+1
How many complex zeros does a degree 4 polynomial have?
<p>4</p>
Let f(x) = 2x + 1 and g(x) = x2.
Find:
(f ∘ g)(2)
g(2) = 4, then f(4) = 2(4) + 1 = 9. So (f ∘ g)(2) = 9
What is the axis of symmetry of
f(x)=-2(x+1)^2+5
x=−1
Describe the end behavior of
f(x)=x^5
Down left, up right
Divde.
(x^3+2x^2-5x-6) ÷ (x+1)
x^2+x-6
If 3+i is a zero of a polynomial with real coefficients, what else must be a zero?
3-i
Let f(x) = 3x − 4 and g(x) = √(x + 1). Find the formula and domain of (f ∘ g)(x).
Solution:
(f ∘ g)(x) = f(g(x)) = 3√(x + 1) − 4.
For the square root to be defined, x + 1 ≥ 0 → x ≥ −1.
Domain: [−1, ∞).
Does the parabola open upward or downward?
f(x)=3x^2-6x+1
Upward
Find the zeros of the polynomial.
f(x)=(x-2)^2(x+1)
x=2, x=-1
Find the remainder using the Remainder Theorem.
f(x)=2x^2-3x+1
(x-2)
3
List all possible rational zeros of
f(x)=2x^3-3x-1
±1, ±1/2
Question 3
The function h(x) is defined by:
h(x) =
−2x + 3, if x < 1
x2, if x ≥ 1
Find the value of h(2).
Solution:
Since 2 ≥ 1, use the rule h(x) = x².
h(2) = 2² = 4.
Write
f(x)=x^2+6x+4
in vertex form.
f(x)=(x+3)^2−5
At x=2, does the graph cross or touch the x-axis?
f(x)=(x-2)^2(x+1)
Touch
Is the following a factor?
x-3
f(x)=x^3-3x^2+4x-12
Yes
Write a polynomial with zeros 2 (multiplicity 2) and -3.
(x-2)^2(x+3)
True or False:
The function p(x) is defined as:
p(x) =
x + 2, if x < −1
3, if −1 ≤ x < 2
−x + 5, if x ≥ 2
is continuous at x = −1.
Find the maximum or minimum value of
f(x)=−x^2+8x−3
Maximum value is 13
What is the maximum number of turning points for a degree 5 polynomial?
4
Write a polynomial with zeros 2 and -1.
(x-2)(x+1)
Find all zeros of the polynomial, given that x=2 is a zero.
x^3-4x^2+x+6
x=-1, 2, 3
Find the difference quotient
(f(x+h)-f(x))/h
for the function
f(x) = 3x^2 - 5x + 1
6x-5