How do you find the coordinates of the vertex #y= -3x^2 + 8x#?

Answer 1

#(4/3,16/3)#

The #color(blue)"standard quadratic function"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=ax^2+bx+c; a≠0)color(white)(2/2)|)))#
#"for "y=-3x^2+8x#
#a=-3,b=8" and "c=0#

The x-coordinate of the vertex can be found using.

#color(red)(bar(ul(|color(white)(2/2)color(black)(x_("vertex")=-b/(2a))color(white)(2/2)|)))#
#rArrx_("vertex")=-8/(-6)=4/3#

Substitute this value into the equation to obtain the corresponding y-coordinate.

#y_("vertex")=-3(4/3)^2+8(4/3)#
#color(white)(y_("vertex"))=(-3xx16/9)+32/3#
#color(white)(y_("vertex"))=-16/3+32/3#
#color(white)(y_("vertex"))=16/3#
#rArr"coordinates of vertex "=(4/3,16/3)# graph{-3x^2+8x [-20, 20, -10, 10]}
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Answer 2

To find the coordinates of the vertex of the quadratic function y = -3x^2 + 8x, you can use the formula x = -b / (2a) to find the x-coordinate of the vertex, where 'a' is the coefficient of the x^2 term and 'b' is the coefficient of the x term in the quadratic equation. Once you have the x-coordinate, substitute it back into the original equation to find the corresponding y-coordinate. So, for the given equation y = -3x^2 + 8x, 'a' = -3 and 'b' = 8. Substitute these values into the formula x = -b / (2a) to find the x-coordinate of the vertex. Then, substitute this x-value into the original equation to find the corresponding y-coordinate. Therefore, x = -8 / (2 * -3) = 8 / 6 = 4 / 3. Then, substitute x = 4 / 3 into the original equation to find y: y = -3(4/3)^2 + 8(4/3) = -3(16/9) + (32/3) = -16/3 + 32/3 = 16/3. So, the coordinates of the vertex are (4/3, 16/3).

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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.

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.

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.

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.

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