Questions: Consider the following function. a(x) = (x-7)(x+3)+25 Step 2 of 3: Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s). How many x-intercepts does this function have? None One Two

Consider the following function. a(x) = (x-7)(x+3)+25 Step 2 of 3: Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s). How many x-intercepts does this function have? None One Two
Transcript text: Consider the following function. \[ a(x)=(x-7)(x+3)+25 \] Step 2 of 3 : Find the $x$-intercepts, if any. Express the intercept(s) as ordered pair(s). Answer Selecting an option will display any text boxes needed to complete your answer. How many $x$-intercepts does this function have? None One Two
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Solution

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Solution Steps

Step 1: Define the Function

The function is given by \[ a(x) = (x - 7)(x + 3) + 25. \]

Step 2: Set the Function to Zero

To find the \( x \)-intercepts, we set the function equal to zero: \[ (x - 7)(x + 3) + 25 = 0. \]

Step 3: Solve for \( x \)

Solving the equation yields: \[ x = 2. \] Thus, the \( x \)-intercept is at the point \[ (2, 0). \]

Final Answer

The function has one \( x \)-intercept, which is \(\boxed{(2, 0)}\).

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