In each case find a quadratic function whose graph passes th

In each case, find a quadratic function whose graph passes through the given points. (If there is no solution, enter NO SOLUTION.) (a) (0, 0), (1, 1) and (9, -55) y = -0.6389x^2 - 2.7692x (b) (-1, 1), (1, -2) and (3, 6) y = (c) (2, -3), (3, -4) and (5, -9) y = (d) (0, 5), (3, 5) and (3, 4) y = NO SOLUTION

Solution

(0,0) , (1,1) , (9,-55)

We can write it as :

y = ax^2 + bx + c

Using (0,0) :
0 = 0 + 0 + c
c = 0

So, we have
y = ax^2 + bx

Now, using (1,1) :
1 = a+ b

And using (9,-55) :
81a + 9b = -55

Now, we have...

a + b = 1
81a + 9b = -55

Solving, we get :
81a + 81b = 81
81a + 9b = -55

Subtract :
72b = 136
b = 136/72
b = 17/9

And using a+ b = 1,
we have
a = -8/9

So, equation is :

y = (-8/9)x^2 + (17/9)x