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)

The x-intercepts of the quadratic equation are x = 3/2 and x = 1.

Step-by-step explanation:

To find the X - intercepts of the graph, you could factor this function and set the remaining pair of binomials to zero in order to get your answer. Remember, the x - intercepts of any graph, including quadratic, is when the y value of that coordinate is zero.

2x^2 - 5x + 3 has a value that is not equal to 1 as an "a" value. In order for us to factor this equation, we will have to multiply the a and c values in order for us to get a new c value to factor: 2 x 3 = 6.

Two numbers that add up to -5 and multiply to 6 are -2 and -3. So, we have are two binomials, 2x^2 -2x -3x + 3. We essentially just broke down the middle term "-5x" into two terms that multiply to 6 and add up to -5. We can then put the binomials together and factor out a common factor: (2x^2 -2x) - (3x+3) 2x(x-1) - 3(x-1) 2x and -3 are common factors of their corresponding binomials, (x-1) cancels out once, and we are left with

(2x-3)(x-1) as our final answer. Wait, we were asked to find the x - intercepts, meaning that we have to set both our binomials to zero:

(2x-3) = 0

    +3    +3

2x/2 = 3/2

x = 3/2

(x-1) = 0

  +1    +1

x = 1

*I would do Part B and C in another answer.