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Quadratic equation y= (x+4)^2 -2

I need to know if it’s Max or min
Domain
Range
Increasing interval
Decreasing interval

Whoever the first correct answer belongs to gets a crown :) tysmmm

Quadratic equation y= (x+4)^2 -2 I need to know if it’s Max or min Domain Range Increasing-example-1
User Sgcharlie
by
7.5k points

1 Answer

7 votes

Answer:

Max or Min: min

Domain: (−∞, ∞)

Range: (−2, ∞)

Increasing interval: (−4, ∞)

Decreasing interval: (−∞, -4)

Explanation:

Max or Min: You determined that the curve opens upwards meaning that the vertex is at the min. If it opened down then it would be at the max.

In mathematical terms: if a > 0, the parabola opens upward and the vertex is a minimum. If a < 0, the parabola opens downward, and the vertex is a maximum.

Domain: This is all possible x values, since the parabola is upwards its going to have any possible x values

Range: this is all possible y values. we know that the vertex point (min) doesn't go less than the value of -2 for y but anything above is possible hence -2 is the lowest possible y value and anything beyond above

Increasing interval: The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I.

Decreasing interval: The derivative, then set it equal to 0, and then find between which zero values the function is negative.

visual representation attached as well

Hope it helps :)

If you have any questions or anymore help lmk, happy to help with any school work!!

Have a nice day, you got this !!

Quadratic equation y= (x+4)^2 -2 I need to know if it’s Max or min Domain Range Increasing-example-1
User Miguel Isla
by
7.6k points