How do you find the vertex and the intercepts for #f(x) = 7 - x^2#?

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Answer 1 · 2016-05-06T22:16:53

This is a parabola with the #y-axis# as the axis of symmetry. It is an 'up-side down' parabola with a maximum turning point.

This is probably easier understood if we write it in the form

#y = -x^2 +7#

There is no #x-#term, which means that the graph is symmetrical about the #y#-axis.

The constant term indicates the #y#-intercept which happens to be the maximum turning point as well. (0,7) graph{y=-x^2+7 [-10, 10, -5, 5]}

To find the #x-#intercepts, make #y# = 0 and solve.

#-x^2 + 7 = 0# #rArr x^2 = 7#

#x = +-sqrt7#