Question

Y = 3x2 − 18x − 19.

Answer 1

Answer:

  A) y = 3(x -3)^2 -46

  B) (3, -46)

  C) look at the y-coordinate of the vertex

Step-by-step 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

__

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).

__

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.