What is the axis of symmetry for the parabola given by the equation y = -2x^2 +

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Question: What is the axis of symmetry for the parabola given by the equation y = -2x^2 + 4x + 1?

Options:

Correct Answer: x = 1

Solution:

The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = -2, b = 4, so x = -4/(2*-2) = 1.

What is the axis of symmetry for the parabola given by the equation y = -2x^2 + 4x + 1?

What is the axis of symmetry for the parabola given by the equation y = -2x^2 + 4x + 1?

Step 1: Identify the coefficients a and b from the equation y = -2x^2 + 4x + 1. Here, a = -2 and b = 4.
Step 2: Use the formula for the axis of symmetry, which is x = -b/(2a).
Step 3: Substitute the values of a and b into the formula: x = -4/(2 * -2).
Step 4: Calculate the denominator: 2 * -2 = -4.
Step 5: Now substitute this back into the equation: x = -4 / -4.
Step 6: Simplify the fraction: x = 1.
Step 7: The axis of symmetry for the parabola is x = 1.

Axis of Symmetry – The axis of symmetry for a parabola is a vertical line that divides the parabola into two mirror-image halves, calculated using the formula x = -b/(2a) from the standard quadratic form.
Quadratic Equation – Understanding the standard form of a quadratic equation (y = ax^2 + bx + c) and identifying coefficients a, b, and c.