# How do you find the vertex and intercepts for f(x)=9x^2+7x+5?

Jan 3, 2016

vertex = ( -7/18 , 95/36 )
there are no intercepts with the x-axis

#### Explanation:

x- coordinate of vertex = -b/(2a

compare $9 {x}^{2} + 7 x + 5 w i t h$ ax^2 + bx + c 
here a= 9 , b = 7 and c =5

so x-coord = $- \frac{7}{18}$

now evaluate $f \left(- \frac{7}{18}\right)$

$= 9 {\left(- \frac{7}{18}\right)}^{2} + 7 \left(- \frac{7}{18}\right) + 5$
$= \frac{49}{36} - \left(\frac{49}{18}\right) + 5$
$= \frac{95}{36}$

now check discriminant $\nabla$ for type of roots

$\nabla = {b}^{2} - 4 a c$
= 7^2 -(4 • 9 • 5 )
=49 - 180
= - 131
since discriminant < 0 there are no intercepts