True or false?
Given the basic graph y=x^2 and the transformations: a vertical stretch by three followed by a shift right 4 units, the resulting equation is y=3(x+4)^2
How do you know when to shift left or right when looking at an equation in vertex form?
originally,y=0 at x=0, now y=0 at x=-4. Isn't that a shift left?
Oh...I get it now! Thank you!
The statement "Given the basic graph y=x^2 and the transformations: a vertical stretch by three followed by a shift right 4 units, the resulting equation is y=3(x+4)^2" is false.
To determine the correct equation, we need to understand the effects of the given transformations on the basic graph y=x^2:
1. Vertical Stretch by Three: This means that the graph will be stretched vertically by a factor of 3. In equation terms, this can be represented as multiplying the function by 3. So, the equation becomes y = 3x^2.
2. Shift Right 4 Units: This means that the entire graph will be shifted 4 units to the right. In equation terms, this can be represented as replacing x with (x - 4). So, the equation becomes y = 3(x - 4)^2.
Therefore, the correct equation for the given transformations is y = 3(x - 4)^2, not y = 3(x + 4)^2 as stated in the original statement.
To arrive at this answer, it is essential to understand the effects of each transformation on the graph and apply them in the correct order.