algebra 2a - projects

which transformation reflects f(x) = (x - 1)^2 + 1 over the y-axis?

XXX f'(x) = (0.1x - 1)^2 + 1)

project 3

dividing polynomials with technology

project 2

exploring dilations of polynomials

what happens to the function f(x) = (x - 1)^2 + 1 when it becomes f'(x) = 1/2((x - 1)^2 + 1)?

it is compressed towards the x-axis

what happens to the function f(x) = (x - 1)^2 + 1 when it becomes f'(x) = 2((x - 1)^2 + 1)?

it is stretched away from x-axis

sarah enters the following into the cas. what did sarah do wrong?

she used "divide" instead of "division."

calculate the quotient. x^3 - 7x + 14 ÷ x + 4

x^2 - 4x + 9 - 22/x+4

calculate the quotient. 5x^7 − 18x^5 ÷ x^2 − 2

5x^5 - 8x^3 - 16x - 32x/x^2-2

consider the division problem. 9x^4 + 2x^3 ÷ x + 10 enter the division problem as you would in the cas tool.

Division(9x^4+2x^3,x+10)

what happens to the function f(x) = (x - 1)^2 + 1 when it becomes f'(x) = (2x - 1)^2 + 1?

XXX it is stretched away from the y-axis

if a quadratic function has a dilation rule in the form f'(x) = af(1/bx)^2, what will cause a vertical dilation?

changing the value of a

if a quadratic function has a dilation rule in the form f'(x) = af(1/bx)^2, what will cause a horizontal dilation?

changing the value of b

if a quadratic function has the rule f(x) = (x − h)^2 + k, what will cause a horizontal translation?

changing the value of h

if a quadratic function has the rule f(x) = (x − h)^2 + k, what will cause a vertical translation?

changing the value of k

project 1

exploring translations of polynomials

consider the graph of function f(x) = x^4. which change in the function rule will translate f(x) to the left?

f'(x) = (x + 9)^4

consider the graph of function f(x) = x^3. which change in the function rule will translate f(x) to the right?

f'(x) = (x - 8)^3

which transformation reflects f(x) = (x - 1)^2 + 1 over the x-axis?

f'(x) = -1.4((x - 1)^2 + 1)

what happens to the function f(x) = (x - 1)^2 + 1 when it becomes f'(x) = (1/3x - 1)^2 + 1?

it is stretched away from y-axis

what happens to the function f(x) = x^2 when it becomes f(x) = x^2 - 3?

it moves 3 units downward.

what happens to the function f(x) = x^4 when it becomes f'(x) = x^4 + 5?

it moves 5 units upward.

johnathan enters the following into the cas. what is the quotient of the problem that he entered?

x^2 - 11x + 60 - 358/x+6