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The function h(x) = x2 + 6x + 7 represents a parabola.

Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)

Part C: Determine the axis of symmetry for h(x). (2 points)

Respuesta :

barnuts

Part A.

The given equation is:

y = x^2 + 6x + 7

By completing the square:

y = (x^2 + 6x + 9) + 7 – 9

y = (x + 3)^2 – 2

y + 2 = (x + 3)^2

 

Part B.

The vertex form of a parabola is in the form:

y – k = 4p (x – h)^2

Where (h, k) is the vertex (x, y) of the parabola.

Therefore the vertex: (-3, -2)

Since 4p = 1, a positive number, therefore the parabola opens up which makes the vertex (-3, -2) the minima of the graph.

 

Part C.

The Axis of Symmetry is the x - coordinate of the vertex which is x = - 3

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