Question

Find an equation of the parabola that has the indicated vertex and whose graph passes through the given point Vertex: ( 2, -1) ; point: ( 4, -3)

Answer 1

The info you have so far is like this on a graph:So it obviously opens downward, right?

Answer 2

It is in the form of y = -x^2. Now put in your vertex and adjust it accordingly.

Answer 3

y = -(x-2)^2 -1

Answer 4

so that's the answer?

Answer 5

let me do some thinking about how to work in the point. No thats' not the whole answer...yet, ok?

Answer 6

ok

Answer 7

Re-do here!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Let me get my act together and post this one more time! Here it is for real! (I was combining this problem on my paper with another one from earlier and didn't realize it! Hence, a huge messed up mess!)

Answer 8

Basic formula for this parabola, using A as the coefficient:\[y=-A(x-h)^{2}+k\]Since your vertex is at (2, -1), that is filled in like this, so far:\[y=-A(x-2)^{2}+1\]

Answer 9

Now you use your point (4, -3) by filling in -3 for y in your basic equation, and filling in 4 for x in your basic equation, like this, solving for A in the process:

Answer 10

\[-3=-A(4-2)^{2}+1\]which gives us\[-3=-A(2)^{2}+1\]\[-3=-4A+1\]Subtract 1 from both sides, then divide by -4 to get A.\[-4=-4A\]and A = 1. But even though your A is positive here, it is a negative parabola, so the negative still goes there. your final equation is this:

Answer 11

\[y=-(x-2)^{2}+1\]

Answer 12

SO SORRY FOR ALL THE CONFUSION!!!! I kept wondering why the numbers were changing every time I looked down at my writing! Too much chicken scratch with way too many x's and y's!