What is the vertex form of # 7y = -3x^2 + 2x − 13#?
The general vertex form is Given Dividing both sides by Extracting the "inverse stretch" coefficient, Completing the square Simplifying For verification purposes here is the graph of the original equation and the calculated vertex point:
for a parabola with vertex at
which is the vertex form with vertex at
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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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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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