1. Perform a series of connected, algebraic, equal successions to simplify each complex number expression
a) (3??-2)(4-5??) b) (?? + 8) / (2- ??)? c)??^95
2. Given the quadratic function f(x)=-(x-3) ^2 +16.Perform the following:
a) Write the vertex of the parabola. Expand the equation to express in general form. ?
b) Find the y-intercept and the x-intercepts. Show all work. Make a table of vertex points. ?
c) Plot and label the vertex, y-intercept, x-intercepts and the axis of symmetry on the x-y plane. ?
d) Use vertex points to find additional points. Label point symmetric to y-intercept. ?
e) Connect points to form parabola. Write equation on the graph.
3. Given the parabolic function g(x) 2x2 + 16x + 24 , perform the following:
a) Find they-intercept and the x-lritercepts. Show all work. Make a table of vertex points, b) Complete the square to find the quadratic In vertex form. Write the vertex.
c) Plot and label the vertex, y-intercept, x-intercepts and the axis of symmetry on the x-y plane.
d) Use vertex points to find additional points. Label point symmetric to y-intercept. e) Connect points to form parabola. Write equation on the graph.
4. Given the quadratic function h(x) 3= 3x2 - 12x - 4 , perform the following:
a) Find the y-intercept. Use algebraic formula to find the coordinates of the vertex. Show all work.
b) Use algebraic formula to find x-intercepts. Write in simplified form and as a decimal in hundredths. c) Plot and label the vertex, y-intercept, x-intercepts and the axis of symmetry on the x-y plane.
d) Make a table of vertex points and use to find additional points. Label point symmetric to y-intercept. e) Connect the points to form a parabola. Write the equation of the parabola on the graph.
5. Given vertex = (-3, 8) and y-intercept = (0, -10) of a parabolic function, perform the following:
a) Use given points to find d(x)= the equation of the parabola in vertex form.
b) Find the x-intercepts. Make a table of vertex points. How does the parabola open and why?
c) Plot and label the vertex, y-intercept, x-intercepts and the axis of symmetry on the x-y plane.
d) Use vertex points to find additional points. Label point symmetric to y-intercept.
e) Connect points to form parabola. Write equation on the graph.
6. Given the following p(x)= x^4 + 2x^3 -7x^2 - 8x +12 and p(1)=0, perform the following
a) Use polynomial long division to factor (x). Continue to factor the quotient to linear factors.
b) Write p(x) = in its complete factored form.
c) Show that the given zero follows from your factored p(x) and find the three additional zeros.
d) Make a table of vertex points and use to find additional points. Label point symmetric to y-intercept.
e) Connect the points to form a parabola. Write the equation of the parabola on the graph.