Determine the vertex of the graph of the quadratic function

Question

Assignment

1. Sketch the graph of the quadratic function.

f (x) = x² - 3x

2. Sketch the graph of the quadratic function f (x) = (x + 4)² + 1. Identify the vertex and axis of symmetry.

3. Sketch the graph of the quadratic function f (x) = x² + 2x + 1. Identify the axis of symmetry.

4. Find the standard form of the quadratic function shown below:

5. Determine the vertex of the graph of the quadratic function

f (x) = x² + x + (5/4) 

6. Determine the x-intercept(s) of the quadratic function

f (x) = x² + 4x - 32

7. Write a polynomial that fits the description.

A fifth-degree polynomial with leading coefficient 4.

8. Multiply or find the special product.

(x + 4) (x + 9)

9. Perform the following operation.

Multiply (x² + 2x + 6)  and (x² - 2x + 6).

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

(-8x) (8x + 7)

11.Completely factor the expression.

x⁴ - 4x³

12.Completely factor the expression.

x² - 8x + 16

13.Completely factor the expression.

(t - 1)² - 9

14.Solve the equation and check your solution.

(5x/2) - (x/6) = 14

15.Determine whether the equation 3 (x - 2) = 3x - 6 is an identity or a conditional equation. If conditional, indicate the condition.

16.Solve the equation and check your solution.

67x - 24 = 3x + 8(8x - 3)

17.Solve the quadratic equation by factoring.

x² + 8x + 16 = 0

18.Solve the quadratic equation by factoring.

64x² - 1 = 0

19.Solve the equation and check your solution. (If not possible, explain why.)

{x / (x + 9)} + {9 / (x + 9)} + 2 = 0

20.Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Sketch the line.

(0,0), m = 3

21.Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slopem. Sketch the line.

(-6, 6), m = -2

22.Which equation does not represent y as a function of x?

y = |-8 + 9x²|

x -6y + 5

y = 7x + 9

x = -1

y = √(8 + x)

23.Which of the following equations does not represents y as a function of x?

y = x² - 2

y² = 2 - x

y = x² + 2

y = x² + x - 2

x² + y = 2

24.Which equation does not represent y as a function of x?

-5y² + 7x = 3

2x = -9y

-9x + 7y = -9

-4y = -9

6x² + 7y = -2

25.Find the domain of the function.

h (t) = (3/t)

26.Find the zeros of the function algebraically.

f (x) = √8x - 1

27.Evaluate the indicated function for f (x) = x² - 7 and g (x) = x + 3 

(f - g)(t + 2)

28. Find (f + g)(x)

f (x) = 2x - 4

g (x) = 6 - x

29. Find (f/g)(x)

f (x) = x² + 7x

g (x) = -2 -x

30. Find g ? f

f (x) = x- 3

g (x) = x²