Question

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Answer 1

Answer:

Please find attached the required graph of the equation, y = x² - 2·x - 8, created using MS Excel

Step-by-step explanation:

The given function required to be plot is y = x² - 2·x - 8

Therefore, the coordinates of the vertex of the parabola formed by the equation (h, k) is given as follows;

h = -(-2)/(2×1) = 1

k = 1² - 2×1 - 8 = -9

The coordinates of the vertex = (1, -9)

The roots of the equation is given when y = 0, as follows;

At the roots, we have;

x² - 2·x - 8 = 0

By factorizing, we get

x² - 2·x - 8 = (x - 4)·(x + 2) = 0

Therefore. the roots of the equation are;

x = 4, and x = -2

The coordinates of the roots are;

(4, 0), and (-2, 0)

Two other points can be found at when x = 3 and when x = 0 as follows;

When x = 3, we have;

y = 3² - 2×3 - 8 = -5

(3, -5)

When x  = 0, we have;

y = 0² - 2×0 - 8 = -8

(0, -8)

The five points are;

(1, -9), (4, 0), (-2, 0), (3, -5), (0, -8)

The graph of the equation created using MS Excel showing the five points is attached.