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To find the range of the function y = x² - 3x + 2, we need to determine the set of all possible values that the function can output.
1. Start by finding the vertex of the parabola represented by the quadratic function y = x² - 3x + 2. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a is the coefficient of x² (1 in this case) and b is the coefficient of x (-3 in this case).
2. Calculate the x-coordinate of the vertex:
x = -(-3) / (2*1)
x = 3/2
3. Substitute this x-coordinate back into the original function to find the corresponding y-coordinate:
y = (3/2)² - 3(3/2) + 2
y = 9/4 - 9/2 + 2
y = 9/4 - 18/4 + 8/4
y = -1/4
4. The range of the function y = x² - 3x + 2 is all real numbers greater than or equal to -1/4. This means that the function's output values range from -1/4 to positive infinity.
Therefore, the range of the function y = x² - 3x + 2 is (-1/4, ∞).
