Question

fill in the equation for this function: f(x) = (x - ?)² +

Explanation:

Step1: Identify the vertex form of a parabola

The vertex form of a parabola is \( f(x) = (x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Step2: Determine the vertex from the graph

Looking at the graph, the vertex (the lowest point of the parabola) is at \((4, -3)\). So, \( h = 4 \) and \( k = -3 \).

Step3: Substitute \( h \) and \( k \) into the vertex form

Substituting \( h = 4 \) and \( k = -3 \) into \( f(x) = (x - h)^2 + k \), we get \( f(x) = (x - 4)^2 - 3 \).

Answer:

For the first box (the value of \( h \)): \( 4 \)
For the second box (the value of \( k \)): \( -3 \)
So the equation is \( f(x) = (x - 4)^2 + (-3) \) or simplified \( f(x) = (x - 4)^2 - 3 \)