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Please help this is due soon

Please help this is due soon-example-1

1 Answer

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Answer:

f(x) = 3(x +4)² -6

Explanation:

You want the equation for the parabola shown in the graph with vertex (-4, -6) and additional point (-5, -3).

Vertex form

The vertex form of the equation for a parabola is ...

f(x) = a(x -h)² +k

where the vertex is (h, k) and 'a' is the vertical scale factor.

Application

The vertex is shown on the graph as (h, k) = (-4, -6), so the equation will be of the form ...

f(x) = a(x +4)² -6

The value of 'a' is chosen to make the other given point lie on the graph. Substituting for (x, f(x)), we have ...

-3 = a(-5 +4)² -6

a = 3 . . . . . . . . . . . add 6

The equation of the graph is ...

f(x) = 3(x +4)² -6

__

Additional comment

The point (-5, -3) is 1 unit horizontally and +3 units vertically from the vertex. When the point is 1 horizontal unit away from the vertex, that vertical difference (+3) is the scale factor 'a' in the vertex form equation.

In short, you don't need to solve the equation as we did above, you can read 'a' from the graph.

User Hesam Qodsi
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