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What is the maximum value of 5 - 4x - x2 and the value of x for which the maximum occurs? Explain your answer.​

User Npretto
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1 Answer

3 votes

Answer:

Max value: 9

Max x value: -2

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

User Yahoo
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