Use the function f(x) to answer the questions: f(x) = 2x2 − x − 10

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 = -2, 5/2

B. Minimum

Vertex: (1/4, -81/8)

C. Draw a concave up graph connecting the x-intercepts, vertex and the y-intercept

Step-by-step explanation:

f(x) = 2x² - x - 10

2x² - x - 10 = 0

2x² - 5x + 4x - 10 = 0

x(2x - 5) + 2(2x - 5) = 0

(x + 2)(2x - 5) = 0

x = -2, 5/2

Vertex: (h,k)

h = midpoint of the x-intercepts (due to symmetry)

h = (-2 + 5/2) = 1/4

k = f(1/4)

k = 2(1/4)² - 1/4 - 10 = -81/8

Vertex: (1/4, -81/8)

y-intercept: when x = 0

2(0)² - 0 - 10 = -10

Draw a concave up quadratic connecting thr following points:

(-2,0)

(0,-10)

(1/4,-81/4)

(5/2,0)

A. x = -2, 5/2

B. Minimum

Vertex: (1/4, -81/8)

C. Draw a concave up graph connecting the x-intercepts, vertex and the y-intercept

Step-by-step explanation:

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step-by-step explanation:

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step-by-step explanation:

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