What are the vertex and x-intercepts of the graph of y = x^2 - 6x - 7?

Question

What are the vertex and x-intercepts of the graph of y = x^2 - 6x - 7? Select one answer for the vertex and one for the x-intercepts.
A. Vertex (-3, -16)
B. x-intercepts: (-1, 0), (7, 0)
C. x-intercepts: (1, 0), (7, 0)
D. Vertex (3, -16)
E. Vertex (-3, 20)
F. x-intercepts: (1, 0), (-7, 0)

SnapAndSolve AI · Accepted Answer

Vertex: The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex. Completing the square for y = x^2 - 6x - 7 gives the vertex at (3, -16). Therefore, the correct answer is D. Vertex (3, -16).x-intercepts: To find the x-intercepts, set y = 0 and solve for x: x^2 - 6x - 7 = 0. Factoring gives (x - 7)(x + 1) = 0, so x = 7 and x = -1. Therefore, the correct answer is B. x-intercepts: (-1, 0), (7, 0).

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What are the vertex and x-intercepts of the graph of y = x^2 - 6x - 7?

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