Answer:
Max value: 9
Max x value: -2
Step-by-step explanation:
We're trying to find the vertex of y = 5 - 4x - x²
We can try to convert this equation to vertex form
First, subtract 5 from both sides
y = 5 - 4x - x²
- 5 -5
y - 5 = -4x - x²
Then add -4 to both sides (this is because this the sqaure of half b -4)
y - 5 - 4 = -4x - x²+ 4
y - 9 = -4 - 4x - x²
Factor the right side of the equation
y - 9 = -(x + 2)(x + 2)
y - 9 = -(x + 2)²
Add 9 to both sides
y - 9 = -(x + 2)²
+ 9 + 9
y = -(x + 2)² + 9
To find the max values we have to make it to where x + 2 = 0
x + 2 = 0
- 2 - 2
x = - 2
When we make equation inside the parenthesis 0, we get y = 9
y = -(-2 + 2)² + 9
y = -(0)2 + 9
y = 9
