The vertex is *f*(0) = 0^{2} + 3(0) + 5 = 5
The *y*-intercept is (0, 5). *b*^{2} – 4*ac* = 9 – 4(1)(5) = 9 – 20 = -11
The discriminate is negative, so there are no x-intercepts. You could also tell by seeing that the vertex is above the *x*-axis and *a* is positive, so the parabola points up. *f*(-1) = (-1)^{2} + 3(-1) + 5 = 1 – 3 + 5 = 3
*f*(-4) = (-4)^{2} + 3(-4) + 5 = 16 – 12 + 5 = 9
We need a few extra points, so we've chosen one from each side of the vertex. *x* | *y* | | | 0 | 5 | -1 | 3 | -4 | 9 | 3 | 5 | -2 | 3 | 1 | 9 |
(-3, 5), (-2, 3), and (1, 9) are symmetric to (0, 5), (-1, 3), and (-4, 9). |