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Answer:
Part A: f(x) = 4·x² - 7·x-15 = (x - 3)·(4·x + 5)
Part B: The x-intercepts are x = 3 and -1.25 #
Part C: As x approaches ∞, y approaches ∞, as x approaches -∞, y approaches ∞
Part D: The graph is a u-shaped quadratic equation graph passing though the x-intercept points -1.25 and 3 on the x-axis and the y-intercept point -15 on the y-axis. Both sides of the symmetrical graph curve extending to infinity
Step-by-step explanation:
The function 4·x² - 7·x-15
To factorize the expression, we have at the 0 factors;
Where;
a = 4, b = -7, c -15, substituting gives;
Which gives;
(x - 3)·(x + 1.25) = (x - 3)·(4·x + 5)
f(x) = 4·x² - 7·x-15 = (x - 3)·(4·x + 5)
Part B: The x-intercepts are the point where y = 0, which are x = 3 and -1.25 as shown above
Part C: As x approaches ∞, y approaches ∞, as x approaches -∞, y approaches ∞
Part D: With the the nature of the function as y approaches ∞ and -∞ the graph is a u-shaped graph of a quadratic equation passing though the points -1.25 and 3 on the x-axis and the point -15 on the y-axis.