Question

Im working in a quiz, and I came across a problem in which the vertex form of a function had no a value. I used demos to see if it would still work, but it will take an equation and convert it, so I dont know if theres anything I must do to simplify and make it a true vertex equation. BTW, the question wants me to determine whether the graph will open up or down.

Answer 1

@dude

Answer 2

So would you mind posting the function so I could take a look?

Also, do you know how to convert from standard to vertex form? To determine if the parabola is opening up or down, exam the \(a\) value in standard form or if in vertex form, see if it is postive or negative.

Answer 3

the equations are f(x) = −(x − 1)2 + 5 and g(x) = (x + 2)2 − 3

Answer 4

so im thinking just register the negative in the first equation and register the implied positive in the second

Answer 5

because If a > 0 (positive), then the parabola opens upward and the graph has a minimum at its vertex. If a < 0 (negative), then the parabola opens downward and the graph has a maximum at its vertex.

Answer 6

Yeah right track. But what is the question asking you to do? Is it asking where the functions will intersect?

Answer 7

The functions f(x) = −(x − 1)2 + 5 and g(x) = (x + 2)2 − 3 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.

Answer 8

I just wanted to ensure I wasnt missing anything. I dont recall coming acrossed a vertex form equation without an a value

Answer 9

Ah okay. So algebraically, if the function opens down, the vertex is a maximum. If it opens up, it is a minimum.

Answer 10

at least an obvious a value

Answer 11

yes. and I knew this fact already

Answer 12

You don't really need to know the a value, just look at the sign.

Answer 13

thats what I figured, I just needed some confirmation

Answer 14

Ah okay. Yeah you have the right thinking.

Answer 15

thanks bro