Question 1198798
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The response from the other tutor uses the given vertex and the given other point, along with the vertex form of the equation, to determine the coefficient "a":<br>
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we use the vertex form equation.

f(x) = a(x - h)^2 + k

where (h, k) represents the coordinates of the vertex.

Given the vertex (-1, 6), we substitute the values into the equation:

f(x) = a(x - (-1))^2 + 6

Simplifying further:

f(x) = a(x + 1)^2 + 6

 using the given point (0, 4).

Substitute x and f(x) into the equation:

4 = a(0 + 1)^2 + 6

4 = a(1)^2 + 6

4 = a + 6

a = -2

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If you have a good understanding of the vertex form of the equation of a parabola, then you can find the coefficient "a" with much less work using this shortcut.<br>
The other given point is 1 unit to the right of the vertex. The value 1 unit to the right of the vertex will differ from the value at the vertex by a(1^2) = a.  Since the value at the other point is 2 less than the value at the vertex, the coefficient "a" is -2.<br>
Once you have found the value of "a", then continue as the other tutor does to find the equation in vertex form is<br>
{{{y-6=-2(x+1)^2}}}<br>