Warmup 10-1For the following questions, use the equation, h(t) = -5t2 + 30t + 35.

1. Find the height of the object at 5 seconds, or h(5).

2. What is the initial height of the object?

3. At what time did the object reach its maximum height?

4. What was the maximum height of the object?

5. For what time interval was the object going up?

6. Complete the square for the following equation: x2 – 14x + 33 = 0

7. Complete the square for the following equation: y2 + 20y - 44 = 0

Examples – Circles in Standard Form Part 1

Standard Form for a Circle Equation:

(x - h)2 + (y – k)2 = r2

center of circle is (h, k) (opposite of each number in parenthesis) r = radius of circle (must take square root of r2 to get r )

Writing the equation of a circle in standard form given the center and radius.

Ex. Center = (2.-3) , radius = 6

Ex. Center = (-4, 0), radius = 3

Ex. Center = (7, 8), radius = 10 (remember, squaring a square root cancels it out)

Ex. Center = (5, -1), radius = 23

Given the equation in standard form, identify the center, radius and diameter.

Ex. x2 + y2 = 144 Ex. x2 + (y – 2)2 = 36

Ex. (x + 4)2 + y2 = 81 Ex. (x – 6)2 + (y + 3)2 = 25

Ex. (x + 1)2 + (y – 9)2 = 121

Circles in Standard Form Practice(1)

Write the equation of a circle in standard form for the given information.

1. Center = (0,0) , r = 19 2. Center = (0, 0), r = 210

3 . Center = (0, -7), r = 24 4. Center = (5, 0), r = 37

5. Center = (-1, -4), r = 21 6. Center = (3, -6), r = 47

7. Center = (11, 3), r = 27 8. Center = (-9, 2), r = 3.5

9. Center = (10, -12), d = 14 10. Center = (3, 5), d = 32

11.Center = (0, -6), d = 30 12. Center = (-13, 0) , d = 8

For #13-18, identify the center, radius, and diameter of each circle.

13. (x – 8)2 + y2 = 81 14. x2 + y2 = 289

15. (x - 2)2 + (y + 4)2 = 225 16. (x + 1)2 + (y + 7)2 = 484

17. (x - 5)2 + (y - 12)2 = 4 18. (x + 3)2 + (y – 9)2 = 42