Question

4. (08.07 MC) Which graph shows the quadratic function y = 3x2 + 12x + 14? (5 points) The following graph is labeled A: A four quadrant graph with a parabola opening up, passing through the points negative 3, 1, negative 2, negative 2, and negative 1, 1 with the vertex at 2, negative 2. The following graph is labeled B: A four quadrant graph with a parabola opening up, passing through the points 1, 4, 2, 1, and 3, 4 with the vertex at 2, 1. The following graph is labeled C: A four quadrant graph with a parabola opening up, passing through the points negative 3, 5, negative 2, 2, and negative 1, 5 with the vertex at negative 2, 2. The following graph is labeled D: A four quadrant graph with a parabola opening up, passing through the points 1, 1, 2, negative 2, and 3, 1 with the vertex at 2, negative 2. A B C D

Answer 1

C

Explanation:

You have a vertex of (-2,2) since -b/(2a)=-12/(2*3)=-12/6=-2

and then plug it in for the y-coordinate 3(-2)^2+12(-2)+14=2

So you have a vertex of (-2,2).

The parabola is open up since 3 is positive.

So far it looks like the choice is C because it is the only one that says the vertex is (-2,2) and it does have that it is open up.

Let' s look at (-3,5) and (-1,5).

So if we plug in -3 into 3x^2+12x+14 we get 3(-3)^2+12(-3)+14=5 check mark

what about x=-1? 3(-1)^2+12(-1)+14=5

Bingo! C checks out!