Answer:
The quadratic equation is;
y = 3x^2-7x + 5
when x = 4, y = 25
Step-by-step explanation:
Mathematically, the general form of a quadratic equation is;
y = ax^2 + bx + c
From the first point, we have that x = 0
Thus;
5 = a(0)^2 + b(0) +c
c = 5
Now, in a case when x is 2
3 = a(2)^2 + b(2) + 5
3 = 4a + 2b + 5
4a + 2b = -2 ••••••(i)
when x = 6
71 = a(6)^2 + b(6) + 5
66 = 36a + 6b ••••••(ii)
From equation i,
2b = -2-4a ••••(iii)
we can rewrite equation ii as
66 = 36a + 3(2b)
Substitute iii into ii
66 = 36a + 3(-2-4a)
66 = 36a - 6 - 12a
66 + 6 = 36a -12a
24a = 72
a = 72/24
a = 3
Recall;
2b = -2-4a
2b = -2-4(3)
2b = -2-12
2b = -14
b = -14/2
b = -7
So the quadratic equation would be;
y = 3x^2 -7x + 5
Now let us test;
when x = 10, y = 235
That would be:
y = 3(10)^2 -7(10) + 5
y = 300 - 70 + 5
y = 235
This shows that the derived quadratic equation is correct
Now, when x = 4; we have it that;
y = 3(4)^2 -7(4) + 5
y = 48 -28 + 5
y = 20 + 5 = 25