What is the vertex form of # 7y = -3x^2 + 2x − 13#?

Answer 1

#y=(color(green)(-3/7))(x-color(red)(1/3))^2+(color(blue)(-38/21))#

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

Given #7y=-3x^2+2x-13#

Dividing both sides by #7#
#color(white)("XXX")y=-3/7x^2+2/7x-13/7#

Extracting the "inverse stretch" coefficient, #color(green)m#, from the first 2 terms:
#color(white)("XXX")y=(color(green)(-3/7))(x^2-2/3x)-13/7#

Completing the square
#color(white)("XXX")y=(color(green)(-3/7))(x^2-2/3xcolor(magenta)(+(1/3)^2))-13/7color(magenta)(-(color(green)(-3/7)) * (1/3)^2)#

Simplifying
#color(white)("XXX")y=(color(green)(-3/7))(x-color(red)(1/3))^2+(color(blue)(-38/21))#
which is the vertex form with vertex at #(color(red)(1/3),color(blue)(-38/21))#

For verification purposes here is the graph of the original equation and the calculated vertex point:

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Answer 2

The vertex form of the given quadratic equation is y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.

To convert the given equation into vertex form, first divide each term by 7 to isolate y:

y = (-3/7)x^2 + (2/7)x - 13/7.

Next, complete the square:

y = (-3/7)(x^2 - (2/3)x) - 13/7.

To complete the square inside the parentheses, take half of the coefficient of x, square it, and add/subtract it:

y = (-3/7)[(x - (1/3))^2 - (1/3)^2] - 13/7.

Now, distribute and simplify:

y = (-3/7)(x - (1/3))^2 + (1/7) - 13/7.

Finally, combine constants:

y = (-3/7)(x - (1/3))^2 - 12/7.

So, the vertex form of the equation is y = (-3/7)(x - (1/3))^2 - 12/7.

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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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