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