Answer:
1) A
2) min; min; max; max
3) y = x² + 5x - 3
Step-by-step explanation:
f(x) = x² + 2(x)(5) + 5² - 5² + 24
f(x) = (x + 5)² - 25 + 24
f(x) = (x + 5)² - 1
In ax² + bx + c,
if a > 0, it's a min
if a < 0, it's a max
y = ax² + bx + c
Using (0,-3)
-3 = a(0)² + b(0) + c
c = -3
y = ax² + bx - 3
Using (1,3)
3 = a + b - 3
a + b = 6
Using (-1,-7)
-7 = a(-1)² + b(-1) - 3
-7 + 3 = a - b
a - b = -4
b = a + 4
a + (a + 4) = 6
2a = 2
a = 1
b = 5
y = x² + 5x - 3
Double the side and subtract by 360
11) -x + y = -1 ; 2x - y = 0
y = -1 + x ; 2x - (-1+x) = 0 ⇒ 2x + 1 - x = 0 ⇒x = -1
y = -1 + (-1) ⇒ y = -2
12) -2x + y = -20 ; 2x + y = 48
y = -20 + 2x ; 2x + (-20 + 2x) = 48 ⇒ 2x -20 + 2x = 48 ⇒ 4x = 48 + 20
4x = 68 ⇒ x = 68/4 ⇒ x = 17
y = -20 + 2(17) ⇒ y = -20 + 34 ⇒ y = 14
13) 3x -y = -2 ; -2x + y = 3
y = 3 + 2x ; 3x - (3 + 2x) = -2 ⇒ 3x - 3 - 2x = -2 ⇒ x = -2 + 3 ⇒ x = 1
y = 3 + 2(1) ⇒ y = 3 + 2 ⇒ y = 5
14) x - y = 4 ; x - 2y = 10
x = 4 + y ; (4 + y) - 2y = 10 ⇒ 4 + y - 2y = 10 ⇒ 4 - y = 10
⇒ -y = 10 - 4 ⇒ -y = 6 ⇒ y = -6
x = 4 + (-6) ⇒ x = 4 - 6 ⇒ x = -2
15) x + 2y = 5 ; 3x + 2y = 17
x = 5 - 2y ; 3(5-2y) + 2y = 17 ⇒ 15 - 6y + 2y = 17 ⇒ -4y = 17 - 15
⇒ -4y = 2 ⇒ y = -2/4 ⇒ y = -1/2
x = 5 - 2(-1/2) ⇒ x = 5 + 2/2 ⇒ x = 5 + 1 ⇒ x = 6
The answer is A. X=-1/3 or x=2/3
Answer:
(a) The solutions are: 
(b) The solutions are: 
(c) The solutions are: 
(d) The solutions are: 
(e) The solutions are: 
(f) The solutions are: 
(g) The solutions are: 
(h) The solutions are: 
Step-by-step explanation:
To find the solutions of these quadratic equations you must:
(a) For 





The solutions are: 
(b) For 

The solutions are: 
(c) For 

The solutions are: 
(d) For 


For a quadratic equation of the form
the solutions are:



The solutions are: 
(e) For 




The solutions are: 
(f) For 


The solutions are: 
(g) For 

Using the Zero Factor Theorem: = 0 if and only if = 0 or = 0

The solutions are: 
(h) For 

Using the Zero Factor Theorem: = 0 if and only if = 0 or = 0

The solutions are: 