SOLUTION: Describe the transformations that must be applied to the graph of y= x^2 to obtain the transformed function y= 5(x-4)^2+3. Use mathematical terminology such as reflection, stretch

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Question 1190017: Describe the transformations that must be applied to the graph of y= x^2 to obtain the transformed
function y= 5(x-4)^2+3. Use mathematical terminology such as reflection, stretch, compress, and translate.
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
translate 4 units to the right, compress it 5 fold, and translate the whole graph up 3 units. The lowest point will be at the vertex, the point of which is (-h, k) or (4, 3)
graph%28300%2C300%2C-10%2C10%2C-25%2C25%2Cx%5E2%2C5%28x-4%29%5E2%2B3%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The order of transformations is the order in which you would evaluate y for a given value of x, using PEMDAS order of operations.

Parent function: y=x%5E2

graph%28400%2C400%2C-4%2C12%2C-4%2C10%2Cx%5E2%29

(1) parentheses: (x-4)^2: y=%28x-4%29%5E2 --> translation 4 to the right

graph%28400%2C400%2C-4%2C12%2C-4%2C10%2Cx%5E2%2C%28x-4%29%5E2%29

(2) multiplication: 5(x-4)^2: y=5%28x-4%29%5E2 --> vertical stretch by a factor of 5

graph%28400%2C400%2C-4%2C12%2C-4%2C10%2Cx%5E2%2C%28x-4%29%5E2%2C5%28x-4%29%5E2%29

(3) addition: 5(x-4)^2+3: y=5%28x-4%29%5E2%2B3 --> vertical translation up 3