Question

describe the transformations that occur from the parent function f(x) =x^2 to the function g(x)=2(x+1)^2-7

Answer 1

translate 7 units down. One to the left. The quadratic function stretches vertically by a factor of 2.

Step-by-step explanation:

There are many factors that play transformations in quadratic functions.

Let me give you some rules to help you with transformations.

We know that the standard form for a quad function is y= ax^2+bx+c.

We can write that in vertex form.

The formula is y=a(x-h)^2+k.

a, h, and k can contribute to factors on the graph.

Let's start with a.

When a is greater than 1, the graph stretches vertically, or it is just a stretch.

If a is less than 1 but greater than 0, the graph shrinks or compresses.

A also determines if you have a maximum or minimum as well as if the graph opens up or down.

With h, that plays a role with the horizontal translation.

No specific rules here, but here, the reason why it is one unit to the left and not one unit to the right is because of the formula.

remember how it is x-h. On a graph, it would be -1.

So x--1 is x+1.

Don't get fooled by this.

Vice versa as well.

With vertical translation, however, you do not need to remember anything. If it says -7 it is translated 7 units down from the parent function or y=x^2.

I hope this helps!