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

Question

1070 views around the world

You can reuse this answer
Creative Commons License

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.

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

$x = +-sqrt7$

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