10.9k views
3 votes
Explain how the graph of each given function is a transformation of the graph of

Explain how the graph of each given function is a transformation of the graph of-example-1
User Jaminto
by
8.5k points

1 Answer

4 votes

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

Explain how the graph of each given function is a transformation of the graph of-example-1
Explain how the graph of each given function is a transformation of the graph of-example-2
Explain how the graph of each given function is a transformation of the graph of-example-3
Explain how the graph of each given function is a transformation of the graph of-example-4
User CharlesC
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories