Questions: Find the x-intercepts of the graph of y=(4x+5)(x-4). The x-intercepts are

Transcript text: Find the $x$-intercepts of the graph of $y=(4 x+5)(x-4)$. The x-intercepts are $\square$

Solution

Solution Steps

To find the x-intercepts of the graph of the function $ y = (4x + 5)(x - 4) $, we need to determine the values of $ x $ for which $ y = 0 $. This involves setting the equation equal to zero and solving for $ x $. The x-intercepts occur where each factor of the equation equals zero.

Step 1: Set the Function to Zero

To find the x-intercepts of the function $ y = (4x + 5)(x - 4) $, we set the equation equal to zero: \[ (4x + 5)(x - 4) = 0 \]

Step 2: Solve Each Factor

We solve for $ x $ by setting each factor equal to zero:

$ 4x + 5 = 0 $
$ x - 4 = 0 $

Step 3: Calculate the Solutions

From the first equation: \[ 4x + 5 = 0 \implies 4x = -5 \implies x = -\frac{5}{4} \] From the second equation: \[ x - 4 = 0 \implies x = 4 \]

Step 4: Write the Ordered Pairs

The x-intercepts are the points where $ y = 0 $. Thus, the ordered pairs for the x-intercepts are: \[ \left(-\frac{5}{4}, 0\right) \quad \text{and} \quad (4, 0) \]