Math Final Exam

Write the standard form of the quadratic function whose graph is a parabola with vertex (3,4) and that passes through the point (4,1).

y= a(x-h)^2+k y= -3(x-3)^2 +4

Given function is f(x)= -3(x+1)^2 + 3 (a) Find the vertex in an ordered pair (x,y) (b) Find the x-intercept(s) and y-intercept, and write in an ordered-pair (x,y) (c) Graph f(x) using the information from (a) and (b)

(a) (-1,3) (b) x-intercept- (-2,0) & (0,0) and y-intercept- (0,0) (c) Plot the vertex, x and y intercept

The equation of a circle is given below. x^2 + 8x + y^2 -2y - 64 = 0 (a) Rewrite the equation in standard form (b) Identify the center and the radius

(a) (x+4)^2 + (y-1)^2 = 81 (b) Center- (-4,1) and Radius- 9

The functions f, g, and h are defined as follows. Simplify your answers as much as possible. f(x)= -3 |-8+x| g(x)= -2x^2 + 6/x^2 h(x)= 6+[-2+x Find f(6) Find g(-4) Find h(5)

(a) -6 (b) -13/8 (c) 6+[3

Evaluate each expression. (a) i^23 (b) (8 +[-27) + (4-[-12)

(a) -i (b) 12 + [3i

Suppose the that the function g is defined, for all real numbers, as follows. f(x)= {-3/5x +1 if x> (equal) -1 f(x)= {3 if x<-1 (a) Find f(-3) (b) Find f(-1) (c) Find f(5)

(a) 3 (b) 8/5 (c) -2

The equation of a line is given below. 5x - 4y = 20 (a) Find the slope of the line (b) Find the x-intercept and y-intercept in ordered pairs (x,y)

(a) 5/4 (b) y= -5-->(0,-5) and x= 4-->(4,0) (c) Graph

Consider the polynomial function f(x)= 4x(x-2)^4(x+1)^2. Answer the questions regarding the graph of f. (a) Find the end behavior of the graph of f. (b) Find each real zero of f and multiplicity of each zero. (c) List each real zero of f according to the behavior of the graph at the x-axis near that zero. (d) Find the y-intercept of the graph of f, and write it in an ordered-pair (x,y). (e) Graph a, b, and c

(a) L.C.: 4 positive and Degree: 7 "odd" (b) x=0 (multiplicity of 1), x=2 (multiplicity of 4), and x=-1 (multiplicity of 2) (c) Crosses x-axis at 0 and does not cross the x-axis at 2,-1 (d) (0,0) (e) Plot points

Answer the questions about the quadratic function g(x)= 2x^2 - 8x + 3. (a) Does the function have a minimum or maximum value? (b) Where does the minimum or maximum point in a ordered pair (x,y).

(a) Minimum (b) idk

Suppose that the functions f and g are defined as follows. f(x)= -4x-3 and g(x)= [x+2 (a) Find (f g)(x), and give its domains using interval notation. (b) Evaluate (f-g)(2).

(a) [-2, neg. infinity) (b) -13

For the real-valued functions f(x)= x-4/x-1 and g(x)= 2x-5, find the composition (f g) (x) and specify its domain using interval notation.

(neg. infinity, 1) U (1, infinity)

Solve the absolute inequality. Use interval notation as your answer. | 4x-10 | >(equal) 2

(neg. infinity, 2] U [3, infinity)

Find an equation of the circle whose diameter has endpoints (4,-3) and (3,-1).

(x-4)^2 + (y-3)^2= [17

Find the slope of the line passing through the points (-2,5) and (6,-13).

-9/4

Find all solutions of 2x^2 + 6x + 6 = 0 by using Quadratic Formula.

-b +- [b^2-4ac]/2a -3 - 3i/2 and -3 + 3i/2

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)= 32t-4t^2

64 feet

Solve the inequality. Use interval notation as your answer. 3(3-x)>4-2x

x<5 ( neg. infinity, 5)

Solve for x. 2/x = 3/x-2 - 1

x= -1 and 4

Solve for x. 8x^4 - 32x^2 = 0

x= 0, 2, -2

Solve for x by factoring. (Hint: You must use "factor by grouping") 5x^2 = 11x-2

x= 1/5 and 2

Solve for x. [3x+1] +3 = 10

x= 16

3 | 5x-1 | = 63

x= 22/5 and -4

Solve for x by completing the square. x^2 - 8x= -13

x= 4- [3 and 4+ [3

The entire graph of the function g is shown in the figure below. Find the domain and range of g using interval notation.

Domain is x-axis Range is y-axis

Solve for x. -2x-3(4-2x)=2(x-3)+2

x=4

Determine the interval(s) on which the function is (strictly) decreasing or increasing. Write your answer as an interval or list of intervals.

Look at the domain(x-axis) and range(y-axis)

Solve for x. (3/x-3) - (3/x^2-5x+6) = 2/x-2

No solution

Divide (6x^3 - 16x^2 + 17x - 10)/(3x-2)

Quotient: 2x^2-4x+3 Remainder: -4

Use synthetic division to find the equation (x^3-3x^2+5)/(x-4)

Quotient: x^2+x+4 Remainder: 21

When a graph moves a number of units to the left or right When a graph moves a number of units up or down

Right (negative) Left (positive) Up (positive) Down (negative)

Find the average rate of change of f(x)= -2x^2 - 4x from x1 =-1 to x2 =2. Simplify your answer as much as possible.

f(2)= -16 f(-1)= -2 Average rate of change-4.6 Net change- -14

Find all real zeros of the function f(x)= 3(x+4)^2(x-3)(x^2-81)

Zeros: -4, 3, 9, -9

Find all zeros of the quadratic function y= 15x^2 +x -2

Zeros: 1/3 and -2/5

Solve the compound inequality. Use interval notation as your answer. 1 (equal)< 5x+3/2 < 10

[-1/5,7/5)

A line passes through the point (-3,2) and has a slope of -5/12. Write an equation in slope-intercept form for this line.

b= 3/4 y= -5/12x +3/4

Write the quadratic function f(x)= 2x^2 - 20x + 16 in the form f(x) = a(x-h)^2 +k. Then give the vertex.

f(x)= 2(x-5)^2-34 Vertex: 5, -34

Find the x-intercept(s) and the coordinates of the vertex for the parabola y= -x^2 + 4x - 3. Write them in an ordered pair (x,y).

x-intercept: (1,0) and (3,0) f(x)= -(x-2)^2 + 1 Vertex: (2,1)