Question

Write the quadratic equation in standard form for the following equations (7,4);(-2,1);(1,9)

Answer 1

Answer:

$y=-\frac{7}{18}x^2+\frac{41}{18}x+\frac{64}{9}$

Step-by-step explanation:

We need to write a quadratic equation so we can use standard quadratic equation:

$y=ax^2+bx+c$

Plug the given points to get three equations.

for (7,4), we plug x=7 and y=4

$4=a(7)^2+b(7)+c$

$4=49a+7b+c$ ...(i)

similarly using other two points, we get:

$1=4a-2b+c$ ...(ii)

$9=a+b+c$ ...(iii)

Now we solve those three equations by any method like substitution, or matrices or by any method and get:

$a=-\frac{7}{18},\ b=\frac{41}{18},\ c=\frac{64}{9}$

Now plug these values into $y=ax^2+bx+c$, we get final equation as:

$y=-\frac{7}{18}x^2+\frac{41}{18}x+\frac{64}{9}$