Question

Use the function f(x) = 4x2 − 7x − 15 to answer the questions. Part A: Completely factor f(x). (2 points) Part B: What are the x-intercepts of the graph of f(x)? Show your work. Part C: Describe the end behavior of the graph of f(x). Explain. Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph.

Answer 1

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;

$x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$

Where;

a = 4, b = -7, c -15, substituting gives;

$x = \dfrac{-(-7)\pm \sqrt{(-7)^{2}-4\times 4\times (-15)}}{2\times 4} = \dfrac{7\pm 17}{8} = 3 \ or -1.25$

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.