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What is the vertex form of #y=3x^2-39x-90 #?

Answer 1

Kennedy Adams

Vertex form of equation is # y= 3 (x - 6.5)^2-216.75 #

# y= 3 x^2 -39 x -90# or

# y= 3 (x^2 -13 x) -90# or

# y= 3 (x^2 -13 x + 6.5^2)-3*6.5^2 -90# or

# y= 3 (x - 6.5)^2-126.75 -90# or

# y= 3 (x - 6.5)^2-216.75 #

Vertex is # 6.5, -216.75# and

Vertex form of equation is # y= 3 (x - 6.5)^2-216.75 #

diagram{3x^2-39x-90 [-640, 640, -320, 320]} [Ans]

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Answer 2

Eva Abramson

#y=3(x-13/2)^2-867/4#
#color(white)("XXX")# with vertex at #(13/2,-867/4)#

The general vertex form is #y=color(green)m(x-color(red)a)^2+color(blue)b# with vertex at #(color(red)a,color(blue)b)#

Given: #y=3x^2-39x-90#

extract the dispersion factor (#color(green)m#) #y=color(green)3(x^2-13x) -90#

complete the square #y=color(green)3(x^2-13xcolor(magenta)(+(13/2)^2)) -90 color(magenta)(-color(green)3 * (13/2)^2)#

re-writing the first term as a constant times a squared binomial and evaluating #-90-3 *(13/2)^2# as #-867/4#

#y=color(green)3(x-color(red)(13/2))^2+color(blue)(""(-867/4))#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.