In Exercises 1 and 2, determine whether the statement is true or false. Justify your answer.
1. The graph of f (x) = −12x2 − 1 has no x-intercepts.
2. The graphs of f (x) = −4x2 − 10x + 7 and g(x) = 12x2 + 30x + 1 have the same axis of symmetry.