The point (4,-2) is the vertex of the graph of a quadratic function. The points (8,6) and (2,0) also fall on the graph of the function.

Part A:Complete the graph of this quadratic function by first finding two additional points on the graph.

Part B:What is the y-intercept of the graph?

Part C:What are the x-intercept?

Part D:Find the interval on which the rate of change is always positive.

Part E:What is the sign of the leading coefficient for this quadratic function? How do you know?

The quadratic function has the form f(x) = ax² + bx + c, where a, b, and c are non-zero values, and the calculation of the values can be defined as follows:

Quadratic function:

vertex point of graph function= (4,-2)

points= (8,6) and (2,0)

Using the formula of a quadratic function:

[tex]y = ax^2 + bx + c[/tex]

putting the value into the above-given formula:

[tex]\to (4, - 2), (8, 6), (2, 0)\\\\\to a(4^2) + b(4) + c = - 2\\\\\to 16 a + 4b + c = - 2.........................(a)\\\\\to a(8^2) + b(8) + c = 6\\\\\to 64a + 8b + c = 6......................................(b)\\\\\to a(2^2) + b(2) + c = 0\\\\\to 4a + 2b + c = 0................................(c)\\\\[/tex]

Computing the value of a,b, and c:

[tex]\to a = 0.5\\\\ \to b = - 4 \\\\ \to c = 6\\\\[/tex]

Putting the value of a, b, and c values into the quadratic function:

[tex]\to y = 0.5x^2 - 4x + 6[/tex]

So, the calculated points are:

Part A: (0,6)

Part B: (2,0) and (6,0)

Part C: x>4

Part D: positive the parabola upwards

Please find the correct question and graph file in the attachment.

Find out more about the quadratic function here:

brainly.com/question/5975436