What is the equation of the following graph?

- anonymous

What is the equation of the following graph?

- chestercat

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- anonymous

https://static.k12.com/eli/bb/179/1_17019/2_7354_8_17079/eec3393a134dfa3a7ae7a47f518e5a3db72f35ef/media/5782e5b6e9454cd7f6f7db8cb49fb6219a6e31c9/mediaasset_669401_1.bmp

- anonymous

please help me!

- anonymous

This is just like the other one, except now you have to use the graph to pick out the values. What is the vertex?

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## More answers

- anonymous

(3,-2)?

- anonymous

yes. and the roots?

- anonymous

i'm not sure what the roots are...

- anonymous

the roots are where the graph crosses the x-axis. For example|dw:1434816829118:dw|

- anonymous

What is the x where your parabola crosses?

- anonymous

1 and 5?

- anonymous

yes. Now try plugging the roots into the equation. Remember the form is
\[y = a(x-p)(x-q)\]
Where p and q are the roots

- anonymous

-2=a(3-4)(3-3)?

- anonymous

not quite. We're not using the vertex yet or plugging in for x and y... yet. We have to set up the equation first.
The root are 1 and 5, so plug in 1 and 5 for p and q to get
y = a(x - 1)(x - 5)
*It doesn't matter which is p and which is q*

- anonymous

NOW you plug in the vertex to solve for a

- anonymous

oh, okay. let me try.

- anonymous

-2=a(3-1)(3-5)

- anonymous

yes, now solve it for a

- anonymous

thanks. hold on.

- anonymous

a=1/2?

- anonymous

yes. can I see your final equation to make sure you got the format right?

- anonymous

sure.-2=a(3-1)(3-5)
a=1/2

- anonymous

The a, p, and q are constants that we used properties to find. They are the same for every point on the parabola. The x and y are variables and change for every point, so we need them to stay. So the equation is
y = ½(x -1)(x - 5)

- anonymous

so i solve this equation?

- anonymous

no, that's the answer

- anonymous

thanks again man, this helped.

- anonymous

you're welcome

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