What are the vertex and x-intercepts of the graph of the function given below?y = x2 - 2x - 48A.Vertex: (0, 0); intercepts: x = -4, 6B.Vertex: (1, -49); intercepts: x = 8, -6C.Vertex: (-1, -21); intercepts: x = 6, 4D.Vertex: (1, -40); intercepts: x = 6, 7SUBMITarrow_backPREVIOUS
Question
What are the vertex and x-intercepts of the graph of the function given below?y = x2 - 2x - 48A.Vertex: (0, 0); intercepts: x = -4, 6B.Vertex: (1, -49); intercepts: x = 8, -6C.Vertex: (-1, -21); intercepts: x = 6, 4D.Vertex: (1, -40); intercepts: x = 6, 7SUBMITarrow_backPREVIOUS
Solution
The vertex form of a quadratic function is y = a(x-h)² + k, where (h, k) is the vertex of the parabola.
The standard form of a quadratic function is y = ax² + bx + c.
The given function is y = x² - 2x - 48.
To find the vertex (h, k), we use the formula h = -b/2a. Here, a = 1 and b = -2.
So, h = -(-2)/2*1 = 1.
To find k, we substitute h = 1 into the equation:
k = (1)² - 2*(1) - 48 = 1 - 2 - 48 = -49.
So, the vertex of the function is (1, -49).
To find the x-intercepts, we set y = 0 and solve for x:
0 = x² - 2x - 48
This factors to 0 = (x - 6)(x + 8).
Setting each factor equal to zero gives the solutions x = 6 and x = -8.
So, the x-intercepts are x = 6 and x = -8.
Therefore, the correct answer is:
Vertex: (1, -49); intercepts: x = 6, -8.
However, this option is not listed in your choices. There might be a mistake in the question or the answer choices.
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