# How do you find the vertex of f(x)= -6x^2+ 5x + 18?

Nov 17, 2017

$\left(\frac{5}{12} , \frac{457}{24}\right) \approx \left(0.42 , 19.04\right)$

#### Explanation:

Using:
${v}_{x} = \frac{- b}{2 a}$

${v}_{x} = \frac{- 5}{2 \cdot \left(- 6\right)} = \frac{- 5}{- 12} = \frac{5}{12} \approx 0.42$

and now substituing in the function equation,
$f \left(\frac{5}{12}\right) = - 6 \cdot {\left(\frac{5}{12}\right)}^{2} + 5 \cdot \frac{5}{12} + 18 = \frac{457}{24} \approx 19.04$

so the vertex is point $\left(\frac{5}{12} , \frac{457}{24}\right) \approx \left(0.42 , 19.04\right)$.