Question

I'm having trouble with this, Unfortunately my teacher has a tight schedule tomorrow so I can't ask her, so I decided to come here, can someone clear it up. I'm not looking for the answer just help on it.

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

Explanation:

Part A)

For equation f(x) = 2x² - 5x + 3, to find x intercepts let y=0 then solve x,

2x² - 5x + 3 = 0 -> (2x + 1)(x -3) = 0 , can find x - intercepts from here

x = ____ and ____

Part B)

To find if vertex is a max or min, compare to equation y = ax² + bx +c

if a > 0 then parabola opens up and vertex is a minimum.

if a < 0 then parabola opens down and vertex is a maximum,

thus vertex is a minimum in this problem

to solve vertex set x = -b / 2a = 5 / 2(2) = 5/4

solve for y value

.... vertex is then at point ( 5/4 , y value found)

Part C)

Can plot the intercepts and vertex points