Need Algebra help! ASAP please!

1.) The equation -5x² + 72x + 378 models the number of students enrolled in a school where x is the number of years since the school first opened in 1990. How many students did the school have when it opened?




2.) The equation -5x² + 72x + 378 models the number of students enrolled in a school where x is the number of years since the school first opened in 1990. Which equation can be used to find the year in which 502 students were enrolled?












3.) The equation -5x² + 72x + 378 models the number of students enrolled in a school where x is the number of years since the school first opened in 1990. In which year were 502 students enrolled?








4.) The equation -5x² + 72x + 378 models the number of students enrolled in a school where x is the number of years since the school first opened in 1990. In which year were 502 students enrolled?

1) -5x² + 72x + 378

Replace x with 1

-5 +72 +378 = 445 ANSWER

2) -5x² + 72x + 378 = 502 ANSWER

3) 5x^2 -72x + 124 = 0
5x^2 -10x -62x +124 = 0
5x ( x -2) -62 ( x -2) = 0

( 5x -62) ( x-2) = 0

x = 62/5 OR 2

x = 2

ANSWER YEAR 1991
CHECK
If x = 2
-20 + 144 + 378 = 502

4) 1991

When the school opened, x = 0. y = 378 so there were 378 students.

If there were 502 students, y = 0. Solve -5x² + 72x + 378 = 502

-5x² + 72x + 378 = 502
-5x² + 72x - 124 = 0
5x² - 72x + 124 = 0
By the quadratic formula, x = 2 or x = 12.4
x = 2 means the year is 1992 (2 years after 1990)

1) Since the school opened 1990 and this year is 2012

2012 - 1990 = 22 ( So x is equal to 22 )

- 5 x² + 72 x + 378
= - 5 ( 22 )² + 72 ( 22 ) + 378
= - 5 ( 484 ) + 1584 + 378
= - 2420 + 1206
= - 1214

2) -5x² + 72x + 378
= - 5x ( x ) + 9x (8) + 5 ( 75 )
= ( x + 5 ) ( - 5x + 75)

Hahaha .. sorry! I get dizzy of those kind of questions