Graph this function: f(x) = x^2 −4x − 5 | Steps: Step 1: Identify a and b. | Step 1: | Step 2: Find the vertex using the formula x=−b2ax = \frac {-b}{2a}. x=42(1)x = \frac {4}{2(1)} | Step 2: | Step 3: Plot the vertex. | Step 3: | Step 4: Factor the function to find the x-intercepts. | Step 4: | Step 5: Plot the x-intercepts. | Step 5: | Step 6: Find the y-intercept. | Step 6: | Step 7: Plot the y-intercept. | Step 7: | Step 8: The smooth curve through these points shows the graph of the function. | Step 8: | [(2) =]
For f(x) = x² − 4x − 5, the vertex’s x-coordinate is −b/(2a) = −(−4)/(2·1) = 2. Substitute x = 2 into the function: f(2) = 2² − 4(2) − 5 = 4 − 8 − 5 = −9. So the vertex is (2, −9), and the correct choice is −9.
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