Question

How do you write `y=3x^2-12x+17` in vertex form and identify the vertex, y intercept and x intercept?

Answer 1

x of vertex: `x = (-b/2a) = 12/6 = 2`
y of vertex:`f(2) = 3(4) - 12(2) + 17 = 5`

Vertex form:`f(x) = 3(x - 2)^2 + 5`
To find y-intercept, make x = 0 -> y = 17
To find x-intercept solve `f(x) = 3x^2 - 12x + 17 = 0`
D = 144 - 204 = -60 < 0.
There are no x-intercepts. The parabola graph doesn't intersect the x-axis. It is completely above the x-axis.