A) It Shifts up 5 units
B) It Reflects over the x-axis and elongates it
C) It Translates horizontally to the right 5 units
D) It elongates the parabola
1) Considering y= x² as the parent function. So let's keep the parent function along so that we can compare it to the transformed versions of it:
A) y =x² +5 Parent function shifted up 5 units:
Consider that the c coefficient in a quadratic function points out the point in the y-axis that it's crossed by the parabola.
B) Now examining what the coefficient "a" makes when it comes to transforming the parent function y= x². The greater the coefficient the more elongated the parabola gets. Also, the minus sign before that makes that the parabola gets reflected over the x-axis. In short:
• The greater the coefficient the more elongated the parabola gets
,
• Reflection over the x-axis
C) When we square another term with the x, we translate it to the left or to the right. In this case, since it is -5 then this translates horizontally to the right
d) Finally, when we increase the "a" coefficient from 1 to -3 and raise all that to 2nd power, we elongate the parabola and keep it over the x-axis since it is raised to the 2nd power:
• It Elongates the parabola
Hence, the answer is:
A) It Shifts up 5 units
B) It Reflects over the x-axis and elongates it
C) It Translates horizontally to the right 5 units
D) It elongates the parabola