Question

Y = 3x2 − 18x − 19.

Part A: Show your work to complete the square of the function. (1 point)

Part B: Identify the vertex of the function. (1 point)

Part C: Explain how to determine the maximum or minimum value of the function. (2 points)

Answer 1

A) y = 3(x -3)^2 -46

B) (3, -46)

C) look at the y-coordinate of the vertex

Explanation:

A) Factor the leading coefficient from the variable terms.

y = 3(x^2 -6x) -19

Inside parentheses, add the square of half the x-coefficient. Outside, subtract the same value.

y = 3(x^2 -6x +9) -19 -3(9)

y = 3(x -3)^2 -46

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B) Compared to the vertex form, ...

y = a(x -h)^2 +k

we find a=3, (h, k) = (3, -46).

The vertex is (3, -46).

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C) The vertex is an extreme value (as is any vertex). The sign of the leading coefficient tells you whether the parabola opens upward (+) or downward (-). This parabola opens upward, so the vertex is a minimum.

If the leading coefficient is positive, the y-coordinate of the vertex is a minimum. If the leading coefficient is negative, the y-coordinate of the vertex is a maximum.