A. rewrite the function y = x2 – 14x + 58 in vertex form by completing the square. show your work. b. rewrite the function y = –x2 – 6x – 20 in vertex form by completing the square. show your work. c. does the function y = x2 – 14x + 58 have a maximum or a minimum, and what is it? how about the function y = –x2 – 6x – 20? explain your answers.

A. y = (x -7)² +9

B. y = -(x +3)² -11

C. minimum, (7, 9)

D. maximum, (-3, -11)

Step-by-step explanation:

The general steps to rewriting the function in vertex form are ...

1. factor out the leading coefficient (if not 1) from the first two terms

2. add inside parentheses the square of half the x coefficient; subtract the same amount outside parentheses. The factor in front of the parentheses must be taken into account when adding the same amount outside.

3. rewrite the content of parentheses as a square, collect terms outside parentheses.

___

A. y = x² -14x +58

y = (x² -14x) +58 . . . . . . . . . . step 1

y = (x² -14x +49) +58 -49 . . . step 2

y = (x -7)² +9 . . . . . . . . . . . . . step 3

__

B. y = -x² -6x -20

y = -(x² +6x) -20

y = -(x² +6x +9) -20 -(-9)

y = -(x +3)² -11

__

C. In vertex form, the function for vertical scale factor "a" and vertex (h, k) looks like ...

y = a(x -h)² +k

When a < 0, the vertex is a maximum (the graph opens downward); when a > 0, the vertex is a minimum (the graph opens upward).

The function of part A has a minimum at the vertex (7, 9). 9 is the minimum value.

___

D. The function of part B has a maximum at the vertex (-3, -11). -11 is the maximum value.

domain is all the x values included in the

0 ≤ x ≤ 2

range is all the y values of the graph

-2 ≤ y ≤ 2

***keep in mind that there are different ways to show domain and range

hope this !

~just a girl in love with shawn mendes

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed