Final answer:
The coordinates of the vertex of the parabola given by the equation y = 2x² - 4x + 3 are found using the formula for the x-coordinate of the vertex h = -b/(2a). After calculation, the vertex coordinates are (1, 1), which is not listed in the options provided by the student.
Step-by-step explanation:
The question involves finding the vertex coordinates of a parabola given by the quadratic equation y = 2x² - 4x + 3. The vertex form of a parabola is y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
To find the vertex, we can use the formula h = -b/(2a) to determine the x-coordinate of the vertex, where 'a' and 'b' are coefficients from the quadratic equation. In our case, a = 2 and b = -4. Plugging these values into the formula gives us h = -(-4)/(2*2) = 1. To find the y-coordinate k, we substitute h back into the original equation, y = 2*1² - 4*1 + 3 = 2 - 4 + 3 = 1. Therefore, the coordinates of the vertex are (1, 1).
None of the provided options B) (1,-9) or C) (1,-1) match the correct coordinates of the vertex (1, 1). Hence, the correct answer is not listed among the options provided by the student. The given equation is y = 2x² - 4x + 3. To find the coordinates of the vertex of the parabola, we can use the formula x = -b / 2a.
In this equation, a = 2 and b = -4. Plugging these values into the formula, we have x = -(-4) / (2 * 2) = 4 / 4 = 1. Substituting x = 1 into the equation, we can find the y-coordinate of the vertex: y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1.Therefore, the coordinates of the vertex of the parabola are (1, 1).