When graphing the function y = 2x² - 8x + 5, what is the axis of symmetry?
Understand the Problem
The question is asking for the axis of symmetry of the quadratic function y = 2x² - 8x + 5. The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the standard form of the quadratic equation.
Answer
The axis of symmetry is $x = 2$.
Answer for screen readers
The axis of symmetry is $x = 2$.
Steps to Solve
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Identify coefficients Determine the values of $a$ and $b$ from the quadratic function $y = 2x^2 - 8x + 5$. Here, $a = 2$ and $b = -8$.
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Apply the axis of symmetry formula Use the formula for the axis of symmetry, which is given by: $$ x = -\frac{b}{2a} $$
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Substitute the values Substitute the values of $a$ and $b$ into the formula: $$ x = -\frac{-8}{2 \times 2} $$
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Simplify the expression Simplify the expression: $$ x = \frac{8}{4} = 2 $$
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State the axis of symmetry The axis of symmetry for the quadratic function is $x = 2$.
The axis of symmetry is $x = 2$.
More Information
The axis of symmetry is a vertical line that divides the parabola (the graph of the quadratic function) into two mirror-image halves. For any given value of $x$, there is exactly one corresponding value of $y$ on the parabola.
Tips
- Forgetting to use the correct coefficients from the quadratic equation, which can lead to an incorrect calculation.
- Misapplying the formula for the axis of symmetry, such as forgetting the negative sign on $b$.
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