Question

The graph of the parent function p(x)=x^2 passes through the point E (21,184). The graph p is transformed such that the new graph represents the following function: f(x)=(x+8)^2-5 if this transformation translates point E to a new location what are the cooridinates of E

Answer 1

The new coordinates of E are (13 , 179)

Step-by-step explanation:

Let us revise some transformation

• If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  
• If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)  
• If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k  
• If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k  

∵ p(x) = x²

∵ The graph p is transformed such that the new graph represents

   the function f(x)

∵ f(x) = (x + 8)² - 5

∴ x of p(x) is add by 8 and p(x) subtracted by 5

- By using the 2nd and 4th rule above

∴ The graph of p(x) is translated 8 units left and 5 units down

∵ Point E (21 , 184) lies on the graph of the parent function p(x)

∴ Point p translated 8 units to the left and 5 units down

- That means subtract 8 from its x-coordinate and 5 from its

   y-coordinate

∴ The new coordinates of E = (21 - 8 , 184 - 5)

∴ The new coordinates of E = (13 , 179)

The new coordinates of E are (13 , 179)

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