Find the equation of the quadratic function whose graph is a parabola containing the points(0 ,4)(3 ,19) and(4,68) .
+37158 ax^2 + bx + c = y when x = 0 c = 4 (given as the first point)
ax^2 + bx + 4 = y sub in 3,19
9a + 3b + 4 = 19 and sub in 4, 68
16a + 4b + 4 = 68 now you have two equations and two unknowns ....do you know how to solve these?
various ways ..... multiply first equation by - 1 1/3
-12a -4b - 16/3 = -76/3 add this to the second equation
4a -4/3 = 128/3
4a = 132/3
a = 11 then b = -28
11 x^2 - 28x +4 = f(x)
Here is a graph:
https://www.desmos.com/calculator/bdjis3s6tt
