What are the vertex and x-intercepts of the graph of the function below?y =(x - 4)(x + 2)A.Vertex: (-4, 2); Intercepts: x = 3, -3B.Vertex: (1, -9); Intercepts: x = 4, -2C.Vertex: (1, 9); Intercepts: x = -4, -2D.Vertex: (1, -5); Intercepts: x = -4, 2SUBMITarrow_backPREVIOUS
Question
What are the vertex and x-intercepts of the graph of the function below?y =(x - 4)(x + 2)A.Vertex: (-4, 2); Intercepts: x = 3, -3B.Vertex: (1, -9); Intercepts: x = 4, -2C.Vertex: (1, 9); Intercepts: x = -4, -2D.Vertex: (1, -5); Intercepts: x = -4, 2SUBMITarrow_backPREVIOUS
Solution
The function given is in the form of a quadratic equation y = a(x - h)² + k, where (h, k) is the vertex of the parabola. However, it's not in the vertex form yet. We need to rewrite it.
The given function is y = (x - 4)(x + 2). If we expand this, we get y = x² - 2x - 8.
To find the vertex, we need to complete the square. The x-coordinate of the vertex is given by -b/2a. In this case, a = 1 and b = -2, so h = -(-2)/2(1) = 1.
Substitute x = 1 into the equation to find the y-coordinate of the vertex: y = (1 - 4)(1 + 2) = -3 * 3 = -9. So, the vertex is (1, -9).
The x-intercepts of the graph are the solutions to the equation y = 0. So, we set (x - 4)(x + 2) = 0 and solve for x. This gives x = 4 and x = -2.
So, the vertex is (1, -9) and the x-intercepts are x = 4 and x = -2. The correct answer is B. Vertex: (1, -9); Intercepts: x = 4, -2.
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