Identify the vertex, complete the table and graph g(x)=(x−4)^2−5.

foass77W 2021-02-13 Answered

Identify the vertex, complete the table and graph g(x)=(x4)25.

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Expert Answer

Layton
Answered 2021-02-14 Author has 89 answers

The vertex form of a quadratic equation is y=a(xh)2+k where (h,k) is the vertex.
Comparing y=a(xh)2+k and g(x)=(x4)25 gives h=4 and k=−5. The vertex is then (h,k)=(4,−5).
To complete the table, substitute values of xx on one side of the vertex into g(x) to find the corresponding y-coordinates:
x g(x)
5(54)25=15=4
6(64)25=45=1
7(74)25=95=4
8(84)25=165=11
Plot the vertex and the four points from your table. A quadratic is symmetric about its vertex so plot the mirror images of the four points on the other side of the vertex:

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