Question

(Essay Worth 10 points)
(08.01 HC)
Use the function f(x) to answer the questions:
f(x) = 5x²+2x-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)

Answers

  1. The vertex of the function is a minimum and the coordinate of the vertex of the function is (0.2, -2.4)

    Part A: What are the x-intercepts of the graph of f(x)

    The function is given as:
    f(x) = 5x^2 + 2x – 3
    Expand the function
    f(x) = 5x^2 + 5x – 3x – 3
    Factorize the function
    f(x) = (5x – 3)(x + 1)
    Set the function to 0
    (5x – 3)(x + 1) = 0
    Solve for x
    x = 3/5 and x =-1
    Hence, the x-intercept is 3/5 and -1

    Is the vertex of the graph of f(x) going to be a maximum or a minimum?

    The vertex of the function is a minimum.
    This is so because the leading coefficient of the function is positive

    What are the coordinates of the vertex?

    Here, we have:
    f(x) = 5x^2 + 2x – 3
    Differentiate and set to 0
    10x + 2 = 0
    Solve for x
    x = -0.2
    Substitute x = -0.2 in f(x) = 5x^2 + 2x – 3
    f(0.2) = 5(0.2)^2 + 2(0.2) – 3
    Evaluate
    f(0.2) = -2.4
    Hence, the vertex of the function is (0.2, -2.4)

    What are the steps you would use to graph f(x)?

    To do this, we simply plot the x-intercept and the vertex.
    And then connect the points
    Read more about quadratic functions at:
    #SPJ1

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