Peter K. answered • 01/21/20
Math / Statistics / Data Analytics
Since the vertex is at (-2, 1) and (0,4) is on the parabola, then the parabola points up. By symmetry, (-4, 4) is also on parabola. That would be enough to do a rough sketch; But let's continue:
If we let the parabola be defined by ax^2 + bx + c = y, then because of (0,4), we know that c = 4. We also know that -b/2a = -2 , the axis of symmetry, since -2 is the x coordinate of the vertex.
So b = 4a and we can rewrite the function as ax^2 + 4ax + 4 = y. Plugging in (-2,1), we get:
4a - 8a + 4 = 1= -4a + 4 => a = 3/4, b = 3, so our function is (3/4)x^2 + 3x + 4 = y. Now, given any x, we can get a y to make a great graph. If we put in x = -4, -3, -2, -1, 0, we will get y = 4.00, 1.75, 1.00. 1.75. 4.00; and you can plot those pairs. 5 points is better than the three we got in the first paragraph with no algebra!
