What is the standard form of a quadratic function?
200
In f(x) = x^5 + x^3 + 1, how many possible zeros are there?
5 possible zeros
200
Find the zeros of f(x) = 3x^2 - x -10
-5/3; 2
200
Look at the graph. Name the zeros.
{-1; 0; 3}
200
Use long division (12x^2 + 11x - 56) / (3x+8)
4x - 7
300
Write in Standard Form: y = x^2 + 3x + 1/4
y = (x + 3/2)^2 -2
300
In a polynomial function what must be true for the graph to rise on the left and fall on the right
The highest exponent must be odd and the leading coefficient must be negative.
300
Find the zeros of f(x) = 2x^4 - 2x^2 - 40
+ square root 5 and - square root 5
300
Look at the graph. Write an equation in standard form.
f(x) = 4(x - 2)^2 - 4
300
Use long division (x^3 - 9) / (x^2 + 1)
x + (1/ x^2 +1)
400
Find the vertex for f(x) = (3/5)(x^2 +6x - 5)
vertex is (-3, -42/5)
400
Describe the process to graph a function by hand
1) leading coefficient test
2) find the zeros
3) plot additional points in testing intervals
4) draw graph
400
Find the zeros of f(x) = x^3 - 4x^2 - 25x +100
4, 5, -5
400
Look at the graph.
Tell me three things about graph
-1; 2 are zeros
x = 2 is a repeated zero
the repeat zero has an even exponent because it touches x -intercept.
the graph is a degree of 3
400
Write f(x) = d(x)*q(x) + r if f(x) = x^3 + x^2 - x - 2
and the divisor is (x -2)
x^3 + x^2 - x - 2 = (x - 2)(x^2 + 3x + 5) + 8
500
The number of horsepower y required to overcome wind drag on a car is approx. by y = .002s^2 +.005s - .029,
where is s is the speed of the car. Estimate the maximum speed of the car if the power required to overcome wind drag does not exceed 10 horsepower.
approx 70mph (69.57)
500
f(x)= - (x-1)(x+2)(x-3)^2
name end behavior
name zeros
are there repeated zeros? if so, what are they?what do they mean?
Both left and right fall
1,-2,3
yes; 3; it means the graph touches at x-int but does not pass through
500
Write a polynomial with the given zeros: square root 3, - square root 3, 5
x^3 - 5x^2 - 3x + 15
500
Describe the polynomial function that could represent the graph. Indicate degree of function and leading coefficient
the degree is 4
there is a repeated zero at 0
the leading coefficient is positive
500
Use Synthetic Division (3x^3 -4x^2 + 5)/ (x - 3/2)