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How do you find the vertex of #g(x)=3x^2-24x-110#?

Answer 1

Nathan Axel

THe vertex is at (4,-158)

#g(x)=3x^2-24x-110# we complete the square

#g(x)=3(x^2-8x)-110#

#g(x)=3(x^2-8x+16)-110-48#

We factorise #g(x)=3(x-4)^2-158#

So the vertex is when #x=4##=>#y=-158#

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Answer 2

Eli Assouline

To find the vertex of the quadratic function ( g(x) = 3x^2 - 24x - 110 ), you can use the formula for the x-coordinate of the vertex, which is given by ( x = -\frac{b}{2a} ), where ( a ) is the coefficient of the ( x^2 ) term and ( b ) is the coefficient of the ( x ) term.

In this case, ( a = 3 ) and ( b = -24 ). Plugging these values into the formula gives ( x = -\frac{-24}{2(3)} = 4 ).

To find the y-coordinate of the vertex, substitute ( x = 4 ) into the function ( g(x) ):

[ g(4) = 3(4)^2 - 24(4) - 110 = 12 - 96 - 110 = -194 ]

So, the vertex of the function ( g(x) = 3x^2 - 24x - 110 ) is at the point ( (4, -194) ).

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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.