quadratic functions, algebra homework help
Complete parts a-c for each quadratic function.
a. Find the yintercept, the equation of the axis of symmetry, and the x coordinates of the vertex.
b. Make a table of values that includes the vertex.
c. Use the information to graph the function.
1. f(x) = 3x^2 + 8x
2. f(x) = 2x^2 + 7x + 1
Determine whether each function has a maximum or minimum value. State the maximum or minimum value of each function.
3. f(x) = x^2 + 6x + 9
4. f(x) = x^2 + 4x
5. Write a quadratic equation with roots 3 and 4 in standard form.
Solve each quadratic equation using the method of your choice. Find exact solutions.
6. 1.6x^2 - 3.2x + 18 = 0
7. 10x^2 + 3x = 1
8. x^2 + 8x 48 = 0
Simplify the expression.
9. (5 - 2i) – (8 - 11i)
10. (14 - 5i)^2
Write each equation in vertex form. Then identify the vertex, axis of symmetry, and direction of opening.
11. y = x^2 + 10x + 27
12. y = 9x^2 + 54x 8
Graph each inequality.
13. (x - 5)(x + 7) < 0
14. 5x^2 + x + 2 < 0
Find the exact solution to the system of equations. Check your answer algebraically.
15. y = x^2 - 6x + 1
y + 2x = 6
16. 2x^2 - 4x = y + 1
x + y = 1
