The vertex of the parabola given by the equation y = 2x^2 - 4x + 1 is located at

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Question: The vertex of the parabola given by the equation y = 2x^2 - 4x + 1 is located at which point?

Options:

Correct Answer: (1, -1)

Solution:

To find the vertex, use the formula x = -b/(2a). Here, a = 2, b = -4, so x = 1. Plugging x = 1 into the equation gives y = -1.

The vertex of the parabola given by the equation y = 2x^2 - 4x + 1 is located at which point?

The vertex of the parabola given by the equation y = 2x^2 - 4x + 1 is located at which point?

Step 1: Identify the coefficients from the equation y = 2x^2 - 4x + 1. Here, a = 2 and b = -4.
Step 2: Use the formula for the x-coordinate of the vertex, which is x = -b/(2a).
Step 3: Substitute the values of a and b into the formula: x = -(-4)/(2*2).
Step 4: Simplify the expression: x = 4/4 = 1.
Step 5: Now that we have x = 1, substitute this value back into the original equation to find y.
Step 6: Calculate y by plugging x = 1 into the equation: y = 2(1)^2 - 4(1) + 1.
Step 7: Simplify the equation: y = 2(1) - 4 + 1 = 2 - 4 + 1 = -1.
Step 8: The vertex of the parabola is at the point (1, -1).

Vertex of a Parabola – The vertex of a parabola can be found using the formula x = -b/(2a) and substituting this x-value back into the equation to find the corresponding y-value.
Quadratic Functions – Understanding the standard form of a quadratic function and how to identify coefficients a, b, and c.