determining constant in quadratic

Reecane

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take points A (7/2, 0), B (0,7), C(-7/6, 0) on the xy-plane. The parabola y=-x^2+ax+b is tangent to both lines BA and BC.
a) determine a and b
b) calculate the area of the domain bounded by the line BA, the parabola and y-axis

IS IT EVEN POSSIBLE TO SOLVE THIS?
 
take points A (7/2, 0), B (0,7), C(-7/6, 0) on the xy-plane. The parabola y=-x^2+ax+b is tangent to both lines BA and BC.
Okay, what are lines BA and BC? What are their slopes?

if y=-x^2+ ax+ b then y'= -2x+a. Is there values of a and b such that there are values of x that give those two slopes?

a) determine a and b
b) calculate the area of the domain bounded by the line BA, the parabola and y-axis

IS IT EVEN POSSIBLE TO SOLVE THIS?
If you mean "Is it possible to immediately write down the answer without doing any calculation at all", no, it isn't. You have to use what you know about tangent lines to curves and do the work.
 
IS IT EVEN POSSIBLE TO SOLVE THIS?

Yes; this is a valid exercise. It requires algebra (eg: writing and solving systems of equations) and calculus (eg: determining derivatives and calculating integrals).

Please show us what you've done or thought about thus far.

(My first step would be writing the equations for lines BA and BC, as Halls suggested in his first question to you.)

Also, please read this page, for a summary of our posting guidelines. (In particular, I am curious to know how long it has been since you studied mathematics.)

Cheers :cool:

PS: The exercise improperly uses the word "domain". Replace "domain" with "region".
 
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I came to systems of equations
-x^2+ax+b=y -x^2+ax+b=y
y=-2x+7 y=6x+7

if x=0, then b=7. ok I found b, but i don`t know how to find a. (now I know that it requires calculus, and we dont have calculus at school)
 
Yes; this is a valid exercise. It requires algebra (i.e., writing and solving systems of equations) and calculus (i.e., determining derivatives and calculating integrals).

Please show us what you've done or thought about thus far.

(My first step would be writing the equations for lines BA and BC, as Halls suggested in his first question to you.)

Also, please read this page, for a summary of our posting guidelines. (In particular, I am curious to know how long it has been since you studied mathematics.)

Cheers :cool:

PS: The exercise improperly uses the word "domain". Replace "domain" with "region".

i think it is "region" too ( test is from japanese government, probably they had trouble with translation)
i am at high school, but we study only algebra. when i saw this problem for the first time i thought there was no way to find solution, now i know it just requires some calculus
and i am non-english speaker, so pardon:D
 
I came to systems of equations
-x^2+ax+b=y -x^2+ax+b=y
y=-2x+7 y=6x+7

if x=0, then b=7. ok I found b

The value of b is not 7.

The value of x at the tangent point on line BA is not the same as the value of x at the tangent point on line BC.

Lines BA and BC intersect at a common y-intercept; therefore, x cannot be zero at either tangent to the parabola. (In other words, zero is not a good choice for x.)

My guess is that you're no longer trying to solve this exercise. Let me know if this guess is wrong.

Also, I reviewed your previous thread. Those tests for Japanese-Government Scholarships contain a number of calculus exercises. (I'm still not sure why you're working those tests, but please feel free to create new threads with your thoughts and/or work thus far, if you would like help with more of those exercises.)

Cheers ~ Mark :cool:
 
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