Need help asap! Thanks!

Question

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

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



C. Sketch a graph the function f(x) = 2x² - 2x - 12. Using a paint program or on paper, make sure you label the vertex and the x-intercepts on your graph.

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

Answer 1

2x^2 -2x - 12

2(x^2 -x) - 12

2(x^2 -x + 1/4) -12 -1/2

2(x- 1/2)^2 - 25/2

is in vertex form with vertex = (1/2, -25/2)

2x^2 -2x -12 = (2x +4)(x-3) x =-2, 3 are the x intercept

It's an upward opening parabola with vertex = minimum point, y intercept (0,-12), x intercepts (-2,0), (0,3) axis of symmetry is x=1/2, so another point on the graph is (1,-12), the point reflected over the axis of symmetry plot those 4 points plus the vertex (1/2, -12 1/2) connect the with a smooth curve

range is [-12 1/2, infinity)