Question

graph the parabola with the following properties: vertex at (-3,-4), X intercepts at -1 and -5, y intercept at 5, domain at (infinite ,infinite ), Range at (-4,infinite)

Answer 1

The graph of the parabola is in the image at the end.

How to graph the parabola?

If a parabola has a vertex (h, k) and leading coefficient a, we can write it as:

y = a*(x - h)² + k

Here the vertex is (-3, -4)

y = a*(x + 3)² - 4

And the y-intercept is (0, 5), then we can write:

5 = a*(0 + 3)² - 4

5 = 9a - 4

5 + 4 = 9a

9 = 9a

9/9 = a

1 = a

Then the equation is:

y = (x + 3)² - 4

Now, to plot the parabola, just plot all the given points and draw a parabola that opens up that pass through all the points, the graph of the parabola is in the image below.