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Create an equation that models the transformation of y equals 2x squared to the function in the graph the points are negative 2, 4 negative 1, -2 0, -4 one, negative 2 2, 4

Y = 2 ( x + 4) squared
Y = 2x squared + 4
Y = 2x squared -4
Y=two( x - 4) squared

1 answer

To determine the correct transformation of the function \( y = 2x^2 \) based on the given points, let's first analyze the points you provided:

  • (-2, 4)
  • (-1, -2)
  • (0, -4)
  • (1, -2)
  • (2, 4)

Notice that the y-values are symmetrical about the y-axis, suggesting a transformation related to horizontal shifting. The critical observation is that the vertex of the parabola appears to have shifted from the origin (0,0) and that your maximum and minimum values suggest a vertical flip.

Let's find the vertex of the parabola. The given y-values suggest that the vertex is at (0, -4) since at \( x = 0 \) we have \( y = -4 \).

Now, we can model this transformation from \( y = 2x^2 \) (which opens upwards) to a new function with vertex at (0, -4).

To obtain this transformation:

  1. We are translating downwards by 4 units.

Starting with \( y = 2x^2 \):

  • The transformation to move down by 4 would give us: \[ y = 2x^2 - 4 \]

Now, let’s compare this with the options given:

  1. \( y = 2(x + 4)^2 \)
  2. \( y = 2x^2 + 4 \)
  3. \( y = 2x^2 - 4 \) (This is the correct result).
  4. \( y = 2(x - 4)^2 \)

Based on the analysis, the correct transformation of the function based on the given points is:

\[ \boxed{y = 2x^2 - 4} \]