Questions: Evaluate the variable expression when (a=4), (b=3), and (c=-1). [b^2-2ac]

Transcript text: Evaluate the variable expression when $a=4, b=3$, and $c=-1$. \[ b^{2}-2 a c \]

Solution

Solution Steps

To evaluate the expression $ b^2 - 2ac $ given the values $ a=4 $, $ b=3 $, and $ c=-1 $, substitute the values of $ a $, $ b $, and $ c $ into the expression and perform the arithmetic operations.

Step 1: Substitute Values

We start by substituting the given values $ a = 4 $, $ b = 3 $, and $ c = -1 $ into the expression $ b^2 - 2ac $.

Step 2: Calculate $ b^2 $

Calculate $ b^2 $: \[ b^2 = 3^2 = 9 \]

Step 3: Calculate $ 2ac $

Next, calculate $ 2ac $: \[ 2ac = 2 \cdot 4 \cdot (-1) = -8 \]

Step 4: Combine Results

Now, combine the results from Step 2 and Step 3: \[ b^2 - 2ac = 9 - (-8) = 9 + 8 = 17 \]

Final Answer

The final result of the expression is \$\boxed{17}\$.

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