Question

G(x)=(x−12)²−30.25

1) What are the zeros of the function? Write the smaller x first, and the larger x second.

Answer 1

The zeros of the function G(x) = (x - 12)² - 30.25 are x = 9.75 and x = 14.25.

Step-by-step explanation:

The zeros of a function are the values of x that make the function equal to zero. In the given function G(x) = (x - 12)² - 30.25, we set G(x) equal to zero and solve for x to find the zeros.

Starting with G(x) = (x - 12)² - 30.25 = 0, we first add 30.25 to both sides to isolate the squared term: (x - 12)² = 30.25. Then, taking the square root of both sides gives
`\(x - 12 = \pm √(30.25)\)`. Simplifying the square root of 30.25 gives
`\(x - 12 = \pm 5.5\)`.

Adding 12 to both sides of the equation, we get x =
`12 \pm 5.5`, which leads to two solutions: x = 9.75 and x = 14.25. Therefore, the zeros of the function G(x) = (x - 12)²- 30.25 are x = 9.75 and x = 14.25. These are the values of x that make the function equal to zero, indicating the points where the graph of the function intersects the x-axis.