Question

Determine the value of "a" for the function f(x) = a(x + 5)^2 - 3 that goes through the point (-4, -5).

a. 2
b. 3
c. 4
d. 5

Answer 1

The value of 'a' for the function f(x) = a(x + 5)² - 3, given that it passes through the point (-4, -5), is -2. None of the provided options match this solution, indicating a potential error in the question or options.

Step-by-step explanation:

The question involves determining the value of a for a given quadratic function f(x) = a(x + 5)² - 3 that passes through the point (-4, -5). To solve for a, plug the coordinates of the point into the equation and solve for a.

Here's the step-by-step calculation:

• Substitute the point's x-coordinate (-4) into the function: f(-4) = a(-4 + 5)² - 3.
• Since the y-coordinate is -5 for the point (-4, -5), we have: -5 = a(1)² - 3.
• Now, add 3 to both sides of the equation to isolate the term with a: -2 = a.

Therefore, the value of a is -2. However, this is not an option in the given choices, suggesting there might be a typo in the question or the options provided. Since, as per the question, we need to select from the given options, none of the provided values (a. 2, b. 3, c. 4, d. 5) is correct.