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

x of vertex: $x = \left(- \frac{b}{2} a\right) = \frac{12}{6} = 2$
y of vertex:$f \left(2\right) = 3 \left(4\right) - 12 \left(2\right) + 17 = 5$
Vertex form:$f \left(x\right) = 3 {\left(x - 2\right)}^{2} + 5$
To find x-intercept solve $f \left(x\right) = 3 {x}^{2} - 12 x + 17 = 0$