The curve y=ax2+bx+c passes through (2,5) (3,12) and (-1,-4).find the equation of the curve

Explanation:

You want to first to substitute to form 3 equations.

5=4a+2b+c

12=9a+3b+c

-4=a-b+c

Now solve with whatever way you fell comfortable, I'm going to use elimination.

First eliminate c

7=5a+b

16=8a+4b --> 4=2a+b

Then I'll eliminate b,

3=3a

a=1

Now solve for b and c

7=5+b

b=2

1-2+c=-4

c=-3

Now for the equation:

y=x^2+2b-3

Hope this helps!

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."