Question

What is the equation of the graph below in vertex form, y=a(x – h)2 + k? Using complete sentences, explain how you developed your equation.

Answer 1

The nice thing about vertex form, is that it tells you exactly where the vertex is, and which way the quadratic is oriented just by looking at it. The equation \(a(x-h)^2+k\) means that the vertex of the parabola is at the point \((h, k)\). If \(a\) is positive, the graph opens up, and if \(a\) is negative, the graph opens down.

Answer 2

This question is asking you to go backward. You have a parabola opening down, with a vertex of \((-1, 1)\). Can you tell me what \(h\) and \(k\) are in the vertex form?

Answer 3

I cant figure out

Answer 4

\(h\) is the negative of the x-coordinate in of the vertex, and \(k\) is the y-coordinate. If your vertex is \((-1, 1)\), then\[h=?\]\[k=?\]Does this help?

Answer 5

so the equation is?
I will do the rst i just need th equation

Answer 6

Since the x-coordinate of your vertex is -1, \(h=-(-1)=1\), and since the y-coordinate is 1, \(k=1\). Now we still have to find what \(a\) is.

Answer 7

First, since the parabola is opening downwards, \(a\) is negative. But what's the value?

Well, know the point \((0, 0)\) is on the graph, so we just plug that in to get \[0=a(0+1)^2+1=a+1\]Solving for \(a\), we get \(a=-1\).

Answer 8

so the equation is X^2+x-1=0?

Answer 9

Your form is \[y=a(x-h)^2+k\]where \(a=-1\), \(h=-1\), and \(k=1\).

Answer 10

y=-1(x-1)+1?

Answer 11

Almost. But in the parentheses you have \((x-(-1)\). The negatives cancel each other out, and you would get \((x+1)\)

Answer 12

thanks

Answer 13

What is the equation of the graph below in vertex form, y=a(x – h)2 + k? Using complete sentences, explain how you developed your equation.