Question

The quadratic function f(x) has a vertex at (9, 8) and opens upward. If g(x) = 4(x − 8)2 + 9, which statement is true?

Answer 1

Now, notice g(x), and recall that

$\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})$

that simply means that the vertex for g(x) is at   $\bf g(x)=4(x-\stackrel{h}{8})^2+\stackrel{k}{9}\impliedby (8,9)$

both parabolas are opening upwards, so they look like a "bowl", from up it goes down down down and reaches the vertex the goes back up up up.

the lowest point or vertex is a minimum, as low as it gets, so, which one is greater then?  f(x)'s which is (9, 8)   or g(x)'s which is (8, 9) ?