Question

Find a formula for the quadratic function whose graph has a vertex at(13,6) and a y intercept of y = 19.NOTE: Enter the exact answery =

Answer 1

The general equation of a parabola with vertex (h,k) is

`y=C(x-h)^2+k`

In our case, we have h = 13 and k =6. So we get the equation

`y=C(x-13)^2+6`

Now, to find the value of C, we will use the given y intercept. In the previous equation we should get y=19 if we replace x = 0. So

`19=C(-13)^2+6\text{ = 169C + 6}`

If we subtract 6 on both sides, we get

`19\text{ - 6 = 13 = 169 C}`

If we divide both sides by 169, we get

`C\text{ = }(13)/(169)\text{ = }(1)/(13)`

So the general equation of the given quadratic function is

`y\text{ = }(1)/(13)(x-13)^2+6`