To estimate the x-intercepts of the function \( y = 2x^2 - 12x + 16 \), it's helpful to first find the exact values of the x-intercepts by setting \( y \) to zero and solving for \( x \).
Step 1: Solve for x-intercepts
Set the equation to zero: \[ 2x^2 - 12x + 16 = 0 \]
Step 2: Simplify the equation
You can divide the entire equation by 2 to simplify: \[ x^2 - 6x + 8 = 0 \]
Step 3: Factor the quadratic
Now, we can factor the quadratic equation: \[ (x - 2)(x - 4) = 0 \]
Step 4: Find the solutions
Setting each factor to zero gives: \[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \] \[ x - 4 = 0 \quad \Rightarrow \quad x = 4 \]
Conclusion
The x-intercepts of the function \( y = 2x^2 - 12x + 16 \) are at \( x = 2 \) and \( x = 4 \).
Graphing the function
If you were to graph \( y = 2x^2 - 12x + 16 \), you would see a parabola opening upwards, with intercepts at the aforementioned points (2, 0) and (4, 0). You can use graphing software or a graphing calculator to visualize the function for confirmation.
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