Need help with Vertex Form Asap. Thanks!

Question

1. Write the function f(x) = x² - 4x - 12 in vertex form to highlight the vertex. Enter the function in vertex form and the coordinates of the vertex.

2. Write the function f(x) = x² - 4x - 12 in factored form to highlight the x-intercepts. Enter the function in factored form and the coordinates of the x-intercepts.

3. Sketch a graph the function f(x) = x² - 4x - 12. Using a paint program or on paper (no graphing utilities). Paste or insert a photo of your graph, make sure you label the vertex and the x-intercepts on your graph.

4. Enter the range of the graphed function using proper notation.

Answer 1

Kenneth

1. Vertex form is a (x-h)² + k. Here a = 1. In (x-h)² we need a -4x term, giving h=2 . (x-2)² = x²-4x+4, and we need to subtract 16 to get to f(x). So f(x) = (x-2)² -16, h = 2 k = -16 . vertex = (h,k) = (2, -16)
2. x² - 4x - 12 = (x-6) (x+2) . When y = 0, x-6 = 0 or x+2 = 0, so x = 6 or -2 (x intercepts)
3. Use Desmos or graphing calculator
4. Read off the range (y values) from your graph.

Mike