Which of the following represents the x-intercepts and the vertex of the quadratic relation y = x2 − 4?
Question
Which of the following represents the x-intercepts and the vertex of the quadratic relation y = x2 − 4?
Solution
The x-intercepts of the quadratic relation y = x^2 - 4 are found by setting y to 0 and solving for x.
0 = x^2 - 4 x^2 = 4 x = ±√4 x = ±2
So, the x-intercepts are x = -2 and x = 2.
The vertex of a quadratic relation y = ax^2 + bx + c is given by the point (h, k), where h = -b/2a and k = f(h).
In this case, a = 1 (the coefficient of x^2), b = 0 (since there is no x term), and c = -4.
So, h = -b/2a = -0/(2*1) = 0.
Substituting h = 0 into the equation gives k = f(h) = (0)^2 - 4 = -4.
So, the vertex of the quadratic relation is (0, -4).
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