# College Algebra problems. Must show all work

**Question description**

Please show ALL work

1.Show the graph of the quadratic function
f(x) = x^{2}-4 .
Identify the vertex and axis of symmetry.

2. Show the graph of the quadratic function
f(x) = x^{2}+3 .
Identify the vertex and axis of symmetry.

3. Show the graph of the quadratic function
f(x) = (x+4)^{2}+1 .
Identify the vertex and axis of symmetry.

4. Give the vertex of the graph of the
quadratic functionf(x)= x^{2}+x + 5/4

5. Determine
whether the statement is true or false.

The function given by f(x) = -17x^{2} -6 has no[img width="17" height="29" src="file:///C:/Users/Jenica/AppData/Local/Temp/msohtmlclip1/01/clip_image001.png" alt="mc005-2.jpg" v:shapes="Rectangle_x0020_5">-intercepts.

6. Determine
the*x*-intercept(s) of the quadratic function f(x)= x^{2 }+ 4x-32

8. Perform the operation and write the result in standard form.

8z - [ 3z - (7z+5) ]

9. Perform the following operation.

Multiply
(3x +7) and (x-9)

10. Perform the operation and write the result in standard form.

(9 -
3.5y) {8y^{3}} ( to the third power)

11. Completely
factor the expression. (t -1)^{ 2 }-9

12. Factor
the trinomial by grouping. 15x^{2 } - 16x +1

13. Factor
the trinomial by grouping. t^{2 } -3t-28

14. Determine whether the value of x= -3 is a solution of the equation.

11-5x =5x -10

15. Solve the equation and check your solution.

5y + 1 = 6y -5+ 8y

16. Determine whether the equation -6(x-1) = -6x + 12is an identity or a conditional equation. If conditional, indicate the condition.

17. Write the following quadratic equation in standard form.

-8x^{2 }=3+x

18. Solve the quadratic equation by factoring.

X^{2 } + 4x =32

19. Solve the equation6+y/y + 5+y/y = -7

20. Find the slope-intercept form of the equation of the line passing through the points. Sketch the line. (6,4), (-6,6)

22. Evaluate the function f(x)= 6x-5 at f(1)

25. Find the domain of the function. h(t) = 3/t

27. Find (f-g)(x)

f(x)= x +6, g(x) = x -6

28. Find (fg)(x)

f(x) = x^{2 }, g(x)= 7x-6

29. Evaluate the indicated function for
f(x) = X^{2 } + 3,and g(x)= x-6

(f-g)(4t)

30. Find*g*o*f* and the domain of composite function

f(x)= |x|, g(x) =x+1

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