Solve the equation. x2 = 160
2 answers:
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The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
Step-by-step explanation:
The vertex form of the quadratic equation y = ax² + bx + c is
y = a(x - h)² + k, where
- (h , k) are the coordinates of the vertex point
- a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
- k is the value of y when x = h
∵ y = x² + 16x - 7
∵ y = ax² + bx + c
∴ a = 1 , b = 16 , c = -7
∵
∴
∴ h = -8
To find k substitute y by k and x by -8 in the equation above
∵ k is the value of y when x = h
∵ h = -8
∴ k = (-8)² + 16(-8) - 7 = -71
∵ The vertex form of the quadratic equation is y = a(x - h)² + k
∵ a = 1 , h = -8 , k = -71
∴ y = (1)(x - (-8))² + (-71)
∴ y = (x + 8)² - 71
∵ (h , k) are the coordinates of the vertex point
∵ h = -8 and k = -71
∴ The vertex is (-8 , -71)
The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
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Answer:
The sprinkler can spread water 18 feet away.
Step-by-step explanation:
We are given the following in the question:
Area formed by watering pattern = 1,017.36 square feet
We have to find the how far the sprinkler spread the water.
The sprinkler covers a circular area. We need to find the radius of this circular area to find the how far the sprinkler spread the water.
Area of circle =
Putting values, we get:
Therefore, the sprinkler can spread water 18 feet away.