Algebra 2 Question, in description, it did not fit in the title

Question

For the following quadratic function, algebraically determine each of the following: the direction of opening, axis of symmetry, vertex, y-intercept, and two additional points. Sketch the graph of the function including an appropriate scale, state the domain and range, and identify the intervals that the function values are increasing or decreasing.

1. y=3x^2 + 7x + 1

Answer 1

Find the vertex. The fastest way of doing that is using the equation V_x = -b/2a to find the x-coordinate of the vertex.

"a" is the leading coefficient (3), and "b" is the second coefficient (7). Thus V_x = -7/(2*3) = -7/6

To find the y-coordinate of the vertex, plug in the x coordinate back into the equation:

y = 3(-7/6)² + 7(-7/6) + 1 = -37/12

The leading coefficient is positive, so it opens upwards.

The axis of symmetry is a vertical line that goes through the vertex.

The y-intercept is the point that intercepts the y axis (you can get this point by setting x equal to zero)

The domain is all the possible values of x and the range is all the possible values of y.