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The graph of y = ax^2+ C contains the point (2, 14). Which point lies on the graph of y = a(x - 2)² + c?

User ClydeFrog
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1 Answer

4 votes

Given:

The graph of
y = ax^2+c contains the point (2, 14).

To find:

The point which lies on the graph of
y = a(x-2)^2+c.

Solution:

Consider the given equations are


y_1 = ax^2+c ...(i)


y_2 = a(x-2)^2+c ...(ii)

The translation is defined as


g(x)=f(x+a)

where, a is horizontal shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

From equation (i) and (ii), it is clear that a=-2. So, graph of
y = ax^2+c shifts 2 units right to get the graph of
y = a(x-2)^2+c.

It means each point on
y = ax^2+c shifts 2 units right.


(x,y)\to (x+2,y)

(2, 14) lies on
y = ax^2+c.


(2,14)\to (2+2,14)


(2,14)\to (4,14)

Therefore, (4,14) must be lies on
y = a(x-2)^2+c.

User Anatoly Rr
by
7.9k points

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