QQuestionMathematics
QuestionMathematics
"Find the equation of the axis of symmetry of the following parabola algebraically:
y=−5x^2 + 20x"
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Answer
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Step 1:I'll solve this step-by-step using the precise LaTeX formatting guidelines:
Step 2:: Identify the standard form of a quadratic equation
• Here, $$a = -5$$, $$b = 20$$, $$c = 0
• In this case, y = - 5x^{2} + 20x + 0
Step 3:: Calculate the axis of symmetry formula
x = -\frac{20}{2(-5)}
• Substituting the values:
Step 4:: Simplify the calculation
• $$x = -\frac{20}{-10}
• x = 2
Step 5:: Verify the axis of symmetry
• The vertical line $$x = 2$$ passes through the vertex of the parabola
• This line divides the parabola into two symmetric halves
Final Answer
The equation of the axis of symmetry is x = 2.
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