Answer:
y = - 
(x - 5)² + 7
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (5, 7 ) , then
y = a(x - 5)² + 7
To find a substitute (10, - 3 ) into the equation
- 3 = a(10 - 5)² + 7 ( subtract 7 from both sides )
- 10 = 5²a = 25a ( divide both sides by 25 )
= a , that is
a = -
y = - (x - 5)² + 7 ← in vertex form
Set x as adult tickets.
Set y as children's tickets.
x + y = 15
30x + 20y = 270
Solve for x in the first equation.
x + y = 15
x = 15 - y
Plug this into the second equation.
30x + 20y = 270
30(15 - y) + 20y = 270
450 - 30y + 20y = 270
450 - 10y = 270
-10y = -180
y = 18
If there is 18 childrens tickets, there should be -3 adult tickets.
This is impossible, and this impossible answer occured because the question is written wrong.
There are a total of 15 tickets
The smallest costing ticket is the childrens ticket, which costs 20$.
If he only bought children tickets, this would be 20x15 which is 300$.
300$ is over 270$, which makes the question impossible.
There is no way to factor this so i would assume the answer is no solution.
Chronological order
Hoped this help
