Question

Найдите те значения а и в, при которых точки А(2,-3) И В(1,4) принадлежат параболе y=ax^2+bx.

Answer 1

y=ax^2+bx

 

-3=a*2^2+b*2

4=a*1^2+b*1

 

4a+2b=-3

a+b=4  => a=4-b

 

4*(4-b)+2b=-3 => 16-4b+2b=-3 => -2b=-19 => b=9,5

  a=4-b => a=4-9,5=-5,5

 

y=-5,5*x^2+9,5 

Answer 2

I can help you with your math problem.

To find the values of a and b, you need to substitute the coordinates of the points A and B into the equation of the parabola and solve the system of two equations with two unknowns.

The system is:

$$ \begin{cases} -3 = a \cdot 2^2 + b \cdot 2 \\ 4 = a \cdot 1^2 + b \cdot 1 \end{cases} $$

Solving this system by elimination, we get:

$$ \begin{align*} -3 &= 4a + 2b \\ 4 &= a + b \\ -7 &= 3a \\ a &= -\frac{7}{3} \\ b &= 4 + \frac{7}{3} \\ b &= \frac{19}{3} \end{align*} $$

Therefore, the values of a and b are $-\frac{7}{3}$ and $\frac{19}{3}$ respectively.Ответь+подробно.+Найдите+те+значения+а+и+в,+при+которых+точки+А(2,-3)+И+В(1,4)+принадлежат+параболе+y=ax^2+bx.