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finding equation of graph y=f(x)

this is probabbly really really easy.

But how do i find the equation of the graph in the form y=f(x)

the graph meets the x -aix at 1,0 and 3,0 and the staionary point is 2,-1

the graph is in the form of a positive x^2 graph.
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Avatar for sonofdot
sonofdot
8
If a quadratic graph crosses the x-axis at (a,0) and (b,0), then y = (x-a)(x-b). Expand this and you'll have your equation :smile:
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f45
OP
2
I get that thanks.

why does the answer say before the equation.

f is greater than or equal to -1
Small point to add: The graph is actually of the form y = k(x-a)(x-b) (where k is another constant) - and you might need to use the information on the graph's turning point to find out the value of k.
But in this example, k=1 - so you don't need to worry about it.
f45
why does the answer say before the equation.

f is greater than or equal to -1

Because f(x) = -1 is the lowest value that it can take. Whatever value of x you put into the function, you will always get a result that is greater than or equal to -1.
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f45
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tomthecool
Because f(x) = -1 is the lowest value that it can take. Whatever value of x you put into the function, you will always get a result that is greater than or equal to -1.

is that just for this example?

if not in a similar question would you write f is greater than or equal to (the lowest y-value) if it was a positive x^2 graph.

Thus if it was a negative x^2 graph it would be x is less than or equal to the highest y value?
Reply 6
Avatar for sonofdot
sonofdot
8
f45
is that just for this example?

if not in a similar question would you write f is greater than or equal to (the lowest y-value) if it was a positive x^2 graph.

Thus if it was a negative x^2 graph it would be x is less than or equal to the highest y value?


correct :smile:

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