Question

How do you know if a parabola is showing the maximum or minimum value?

Answer 1

like in the equation.

Answer 2

Suppose you start with a parabola in standard form:
\[y=ax^2+bx+c\]
Completing the square, you can write it in vertex form:
\[y=a(x-h)^2+k\]
where \((h,k)\) is the vertex.

The sign of \(a\) determines if the vertex is a minimum or maximum.

If \(a>0\), then the parabola "opens upward," so the vertex is a minimum.
If \(a<0\), then the parabola "opens downward," so the vertex is a maximum.

Answer 3

heh thats weird because i got a question where to find the minimum but when I drew it, it was opening up

Answer 4

\[y=3(x-16)^{2}+246\]

Answer 5

but the questions is asking to find the minimum value. How do I do that?

Answer 6

Since \(a=3>0\), the parabola opens upward, so the vertex is the minimum. Find the vertex and you'll have your answer.

Answer 7

so the vertex is (16,246)?

Answer 8

Right.

Answer 9

that opening downward tho

Answer 10

Check the plot: http://www.wolframalpha.com/input/?i=3%28x-16%29%5E2%2B246

That's what I mean by opening upward. Maybe you have a different interpretation

Answer 11

nope