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The graph of y=f(x) is a parabola whose vertex is at (1,-2). The graph of y=f(x-3) is also a parabola. Where is the vertex of the graph of y=f(x-3)

Mar 23, 2024

#1
+394
+2

f(x - 3) represents a translation right by 3.

Therefore, the whole graph is shifted right by 3, meaning the vertex shifts right by 3.

Shifting right by 3 means that 3 is added to the x coordinate.

Therefore the new vertex is (1 + 3, -2) = (4, -2).

Alternatively, if you don't know translations: Use vertex form:

\(f(x)=a(x-1)^2-2\) represents a parabola of vertex (1, -2), where a is a constant

\(f(x-3) = a((x-3)-1)^2-2=a(x-4)^2-2\), so looking at this form, you know the vertex is (4, -2).

Mar 23, 2024
edited by hairyberry  Mar 23, 2024

#1
+394
+2

f(x - 3) represents a translation right by 3.

Therefore, the whole graph is shifted right by 3, meaning the vertex shifts right by 3.

Shifting right by 3 means that 3 is added to the x coordinate.

Therefore the new vertex is (1 + 3, -2) = (4, -2).

Alternatively, if you don't know translations: Use vertex form:

\(f(x)=a(x-1)^2-2\) represents a parabola of vertex (1, -2), where a is a constant

\(f(x-3) = a((x-3)-1)^2-2=a(x-4)^2-2\), so looking at this form, you know the vertex is (4, -2).

hairyberry Mar 23, 2024
edited by hairyberry  Mar 23, 2024
#2
+16
+2

Thank you!!

Arhantio  Mar 23, 2024
edited by Arhantio  Mar 23, 2024