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)

A.) x = 3/2 or 1

B.) The coordinate of the vertex will be ( 5/4 , -1/8 )

C.) Find the attached file

Step-by-step explanation:

Given the function

f(x) = 2x2 − 5x + 3

A.) The x - intercept of the graph of the function above will be the root of the function.

Factorise the equation

2x2 − 5x + 3 = 0

Find the two numbers in which the product will be 6 and the sum = -5

The two numbers are -2 and -3

Then,

2x2 − 2x - 3x+ 3 = 0

2x2 − 2x - 3x+ 3 =0

2x( x -1 ) -3( x-1 ) = 0

2x - 3 = 0 or x -1 = 0

2x = 3 or x = 1

Therefore, x = 3/2 or 1

B.) Since the function is positive, that is, the graph will open upward. The vertex of the graph will be minimum

The coordinate of the vertex can be calculated by using the formula

X = -b/2a

Where b = -5 and a = 2

X = 5/( 2×2)

X = 5/4

Substitutes x into the function to get y - coordinate

Y = 2(5/4)^2 − 5(5/4) + 3

Y = 2(25/16) - 25/4 + 3

Y = 25/8 - 25/4 + 3

The LCM of their denominator is 8

Y = (25 - 50 + 24)/8

Y = -1/8

The coordinate of the vertex will therefore be ( 5/4 , -1/8 )

C.) The graph will be a parabola which will be opening upward since it is a positive graph.

The graph will cut across the two roots x = 3/2 and 1 with the minimum at y = -1/8.

Please Find the attached file for the graph.

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step-by-step explanation:

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