Question

HELP PLEASE AND SHOW WORK. write a quadratic function in the form f(x)=a(x-h)^2 + k whose graph has its vertex in the second quadrant. name the vertex, give the equation of the axis of symmetry and tell whether the graph opens up or down, graph your function.

Answer 1

The equation is

• y=(x+3)²+6

As a is positive the parabola opening upwards

(-3,6) is vertex

Axis of symmetry

• x=-3.

Graph attached

Answer 2

The function f(x)=a(x-h)² + k is the parabola with vertex:

• (h, k)

If the vertex is in the second quadrant, the h < 0 and k > 0

It can open up or down, so a ≠0, it opens up if a > 0, opens down if a < 0

The axis of symmetry is the line parallel to y-axis and passing through the vertex, so it would be the line:

• x = h

Now let's assume h = -5, k = 2, a = 1, then our function is:

• f(x) = (x + 5)² + 2

The graph is attached and it opens up as a = 1 > 0

The line of symmetry is

• x = - 5