Question

HELP ME PLEASE PLEASE PLEASE PLEASEEEEEEEEEEEEE

Use the function f(x) to answer the questions:

f(x) = 2x2 − 5x + 3

Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

Answer 1

part A: x= 1 and x= 3/2

part B: minimum at (5/4, f(5/4))

Explanation:

part A: factoring

0 = 2x^2 - 5x + 3

= (2x^2 - 2x)(-3x + 3)

= 2x(x - 1) -3(x-1)

= (2x - 3)(x - 1)

x= 1 and x= 3/2

part B: candidates test

find the derivative of the function.

f(x) = 2x^2 - 5x + 3

f'(x) = 4x -5

solve for critical numbers.

0 = 4x - 5

x = 5/4

candidates test by plugging in numbers into the derivative to see if that area is negative or pos.

f has a minimum at x = 5/4 because f' goes from neg to pos there. to find the coordinate for x = 5/4 just plug it into the original function to find f(5/4).

Part C: to draw the graph, I'd just plot the vertex coordinate that you solved for in part B, then I would plot the x intercepts that you solved for in part a, from there just draw a line throu the 3 points. (it should look like a U shape)