Answer :
Therefore, the graph of y = x^2 - x - 2 is an upward-opening parabola with a vertex at (1/2, -9/4) and x-intercepts at x = 2 and x = -1
To identify the correct key features of the graph of the function y = x^2 - x - 2, we first need to analyze its properties. The function is a quadratic function, which means its graph is a parabola. Since the leading coefficient (the coefficient of the x^2 term) is positive, the parabola opens upwards.
Now, let's determine the vertex of the parabola. The vertex can be found using the formula x = -b/2a, where a and b are the coefficients of x^2 and x, respectively. In this case, a = 1 and b = -1. Thus, the x-coordinate of the vertex is x = 1/2. To find the y-coordinate, substitute the x-value into the equation: y = (1/2)^2 - (1/2) - 2 = -9/4. So, the vertex is at (1/2, -9/4).
Additionally, the parabola has x-intercepts (also known as roots or zeroes), which can be found by setting y = 0 and solving for x: 0 = x^2 - x - 2. Factoring this quadratic equation, we get (x - 2)(x + 1) = 0, and thus the x-intercepts are x = 2 and x = -1.
Therefore, the graph of y = x^2 - x - 2 is an upward-opening parabola with a vertex at (1/2, -9/4) and x-intercepts at x = 2 and x = -1.
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