Respuesta :
Answer: The vertex of the resulting parabola is (A) (-5, 8).
Step-by-step explanation: The given equation of the parabola is
[tex]y=x^2~~~~~~~~~~~~~~~~~~~~(i)[/tex]
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
[tex]y=(x-h)^2+k,[/tex]
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
[tex]y-8=(x+5)^2\\\\\Rightarrow y=(x+5)^2+8,[/tex]
where (-5, 8) is the vertex.
Thus, the vertex of the resulting parabola is (A) (-5, 8).
