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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)
PLEASE HELP MANY THANKS!!!!

Respuesta :

piscezcraft
The X intercepts of the graph are going to be 1 and 1.5. These can be figured out through the quadratic formula.
-(-5)+-V((-5)^2-4(2)(3)) divided by 2(2) getting answers of 1 and 1.5.

The vertex is going to be a minimum as the A value is greater than one, meaning the function will be increasing upwards as X values approach greater / lower values. The coordinates of the vertex will be (1.25, -1.25) the simple way to solve for this is -b/2a. So -(-5)/4 would give 5/4 for the X coordinate of 1.25 then plugging 1.25 into the original function and solving for the Y output, -1.25.

To graph the function you can plot the points of the intercepts and the vertex and then plug in 2 more X values into the function and plot the corresponding X, Y pair to find the general shape of the graph. Hope this could help

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