The graph of f, of, x, equals, 2, x, squaredf(x)=2x 
2
  is given below. Write the equation of a function g, of, xg(x) which would shift the graph of f, of, xf(x) left 6 units.


To shift the graph of \( f(x) = 2x^2 \) left by 6 units, you can replace \( x \) with \( x + 6 \) in the equation. This is because shifting left involves adding a positive value to \( x \).

So, the equation of the function \( g(x) \) will be:

\[
g(x) = 2(x + 6)^2
\]

This represents the graph of \( f(x) = 2x^2 \) shifted 6 units to the left.

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions:
1. What happens when we shift the graph to the right instead of left?
2. How do you shift a graph vertically?
3. How does the shape of the graph change if we change the coefficient of \( x^2 \)?
4. What is the effect of adding a constant to the entire function, rather than inside the parentheses?
5. How would you reflect the graph over the x-axis?

**Tip:** When shifting horizontally, remember that moving left involves adding to \( x \), while moving right involves subtracting from \( x \).

The graph of f(x) = 2x^2 is given below. Write the equation of a function g(x) which would shift the graph of f(x) left 6 units.

This page explains how to shift the graph of the quadratic function f(x) = 2x^2 left by 6 units. The solution involves replacing x with x + 6, yielding g(x) = 2(x + 6)^2. Suitable for students in Grades 8-10 studying graph transformations.

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