# How do you find the vertex of the graph of the function 3x^2-18x+24?

Apr 27, 2017

Vertex of $f \left(x\right) = 3 {x}^{2} - 18 x + 24$ is $\left(3 , - 3\right)$

#### Explanation:

To find the vertex of the graph of function $f \left(x\right) = 3 {x}^{2} - 18 x + 24$, we should convert it into the form $f \left(x\right) = a {\left(x - h\right)}^{2} + k$, where $\left(h , k\right)$ is the vertex.

Hence $f \left(x\right) = 3 {x}^{2} - 18 x + 24$

= $3 \left({x}^{2} - 6 x\right) + 24$

= $3 \left({x}^{2} - 2 \times 3 \times x + {3}^{2} - {3}^{2}\right) + 24$

= $3 {\left(x - 3\right)}^{2} - 27 + 24$

= $3 {\left(x - 3\right)}^{2} - 3$

Hence, vertex of $f \left(x\right) = 3 {x}^{2} - 18 x + 24$ is $\left(3 , - 3\right)$

graph{3x^2-18x+24 [-2.02, 7.98, -3.26, 1.74]}