Deriving Quadratic Equations

Question

Use the given information to determine the most efficient form you could use to write the quadratic function. Then write the quadratic function using algebraic methods(find a, systems of equations, etc)



y-intercept (0,3) and axis of symmetry -3/8

Answer 1

I will assume that the axis of symmetry is x=-3/8

So y=a(x+3/8)² + b

If (0,3) is on the curve, then (-6/8, 3) is on the curve due to the symmetry.

Since you now have two unknowns ( a and b) and two pieces of information ( (0, 3) and (-3/4, 3) ) you can solve for a and b. Give it a try.

Answer 2

-b/(2a) = -3/8

-b/a = -3/4

b/a = 3/4

b = (3/4)a

So the quadratic is ax^2 + (3/4)ax - 3 = 0

4ax^2 + 3ax - 3 = 0

We now need the vertex point (-3/8 , y) or another point (x,y) on the parabola.