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

Dec 10, 2015

Find vertex and intercepts for $f \left(x\right) = 5 {x}^{2} + 9 x + 7$

#### Explanation:

x-coordinate of vertex:
$x = \frac{- b}{2 a} = - \frac{9}{10.}$
y-coordinate of vertex:
$y = f \left(- \frac{9}{10}\right) = 5 \left(\frac{81}{100}\right) - 9 \left(\frac{9}{10}\right) + 7 = \frac{405}{100} - \frac{81}{10} + 7 =$
$= \frac{295}{100} = \frac{59}{20}$
To find y-intercept, make x = 0 --> f(x) = 7
To find x-intercepts make y = 0 and solve $5 {x}^{2} + 9 x + 7 = 0$
$D = {b}^{2} - 4 a c = 81 - 140 < 0$. Since D < 0, there are no x-intercepts.

Dec 10, 2015

Have a look at http://socratic.org/s/aq6riwAj
$\textcolor{red}{\text{It will show you a trick worth remembering!}}$