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

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Answer 1 · 2016-01-03T21:41:30

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

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

compare $9x^2 + 7x +5 with$ ax^2 + bx + c #
here a= 9 , b = 7 and c =5

so x-coord = $- 7/18$

now evaluate $f(-7/18)$

$= 9(-7/18)^2 + 7 (-7/18) + 5$
$= 49/36 - (49/18) + 5$
$= 95/36$

now check discriminant $grad$ for type of roots

$grad = b^2 - 4ac$
# = 7^2 -(4 • 9 • 5 )
=49 - 180
= - 131
since discriminant < 0 there are no intercepts

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