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If we transform y = x2 by 5 units to the left and 8 units up, what is the vertex of the resulting parabola?

(-5, 8)

(5, 8)

(-5, -8)

(5, -8)

Verified Answer :

(-5, 8)

Hope it helps!!!!!!!!!!!!!

Answer:  The vertex of the resulting parabola is (A) (-5, 8).

Step-by-step explanation:  The given equation of the parabola is

\(y=x^2~~~~~~~~~~~~~~~~~~~~(i)\)

We are to find the vertex of the resulting parabola, if the parabola (i) is transformed by 5 units left and 8 units up.

The VERTEX form of a parabola is given by

\(y=(x-h)^2+k,\)

where (h, k) is the vertex.

Now, if we shift parabola (i) by 5 units to the right and 8 units up, then the x-coordinate will increase by 5 units and Y-coordinate will decrease by 8 units.

Therefore, after transformation, equation (i) becomes

\(y-8=(x+5)^2\\\\\Rightarrow y=(x+5)^2+8,\)

where (-5, 8) is the vertex.

Thus, the vertex of the resulting parabola is (A) (-5, 8).

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