What does the equation y = a(x - h)2 + k, a ≠ 0 represent?

you know what y=ax^2 is, right?

Now shift it by (h,k)

how do you shift y=ax^2 by (h,k)

replace y by (y-k) and x by (x-h)

Better review your text where it talks about translation of functions.

The equation y = a(x - h)² + k represents a quadratic function in standard form. It is also called the vertex form of a quadratic equation. Let's break it down to understand its different components:

- "a" represents the coefficient of the quadratic term. The value of "a" determines whether the parabola opens upward (if "a" is positive) or downward (if "a" is negative). It also determines the steepness of the graph.

- "(x - h)²" represents the vertex of the parabola, where (h, k) is the coordinate of the vertex. The value "h" indicates the horizontal shift of the parabola, and "k" indicates the vertical shift.

- "y" represents the output or dependent variable of the function, which corresponds to the vertical coordinate on the graph.

In summary, the equation y = a(x - h)² + k represents a parabolic graph that is shifted h units horizontally and k units vertically from the origin (0, 0). The coefficient "a" determines the shape and direction of the parabola.