Let's determine the correct quadratic function represented by the given table of values.
The quadratic function we're aiming to find should be in the form:
[tex]\[ y = a(x - h)^2 + k \][/tex]
Given the points [tex]\((-3, 3.75)\)[/tex], [tex]\((-2, 4)\)[/tex], [tex]\((-1, 3.75)\)[/tex], [tex]\((0, 3)\)[/tex], and [tex]\((1, 1.75)\)[/tex], we use a method to derive the quadratic function from these points.
The derived values are:
- The coefficient [tex]\(a = -0.25\)[/tex]
- The value of [tex]\(h = -2\)[/tex]
- The value of [tex]\(k = 4\)[/tex]
Let's substitute these values into the quadratic function form:
[tex]\[ y = -0.25(x - (-2))^2 + 4 \][/tex]
[tex]\[ y = -0.25(x + 2)^2 + 4 \][/tex]
So, the equation of the quadratic function represented by the table is:
[tex]\[ y = -0.25(x + 2)^2 + 4 \][/tex]
To select values from the drop-down menus:
- The correct value for [tex]\(a\)[/tex] is [tex]\(-0.25\)[/tex]
- The correct value for [tex]\(h\)[/tex] is [tex]\(-2\)[/tex]
- The correct value for [tex]\(k\)[/tex] is [tex]\(4\)[/tex]
Thus, the completed equation is:
[tex]\[ y = -0.25(x + 2)^2 + 4 \][/tex]
