The equation of a parabola is y=x2+6x+9. Write the equation in vertex form.
1 answer:
Answer:
Step-by-step explanation:
Vertex form is accomplished by completing the square on the quadratic. Do this by first setting the parabola equal to 0 then moving the constant over to the other side:
Now take half the linear term, square it, and add it to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9:
The reason we do this is to create a perfect square binomial on the left:
(obviously the 0 results from the addition of 9 and -9). Move the 0 back over to the other side and set the quadratic back equal to y:
This gives you a vertex of (-3, 0), which is a minimum value, since the parabola opens upwards.
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Answer:
y = 2.31x + 309.35
Step-by-step explanation:
Whenever you are checking for a best fitting equation you want to check if it has a constant slope. If it does then the relation is linear and super easy.
So, since the t values are increasing by the same amount you want to see if the y values are too. And they are, each population entry is increasing by 2.31, this is the slope.
Also, keep in mind you can caluclate slope with the equation here x is replaced by t though.
Now, since we know it's linear and we know the slope we can find the equation with the formula y - y1 = m(x - x1) where again, x is replaced by t and m is the slope 2.31
I am just going to use the first point. so x1 = t1 = 0
y - 309.35 = 2.31(x-0)
y = 2.31x + 309.35
Let me know if there was something you didn't understand.